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3 <title>MayaChemTools:Documentation:Matrix.pm</title>
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14 <table width="100%" border=0 cellpadding=0 cellspacing=2>
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15 <tr align="left" valign="top"><td width="33%" align="left"><a href="./MathUtil.html" title="MathUtil.html">Previous</a> <a href="./index.html" title="Table of Contents">TOC</a> <a href="./AtomsCountDescriptors.html" title="AtomsCountDescriptors.html">Next</a></td><td width="34%" align="middle"><strong>Matrix.pm</strong></td><td width="33%" align="right"><a href="././code/Matrix.html" title="View source code">Code</a> | <a href="./../pdf/Matrix.pdf" title="PDF US Letter Size">PDF</a> | <a href="./../pdfgreen/Matrix.pdf" title="PDF US Letter Size with narrow margins: www.changethemargins.com">PDFGreen</a> | <a href="./../pdfa4/Matrix.pdf" title="PDF A4 Size">PDFA4</a> | <a href="./../pdfa4green/Matrix.pdf" title="PDF A4 Size with narrow margins: www.changethemargins.com">PDFA4Green</a></td></tr>
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16 </table>
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17 </div>
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18 <p>
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19 </p>
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20 <h2>NAME</h2>
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21 <p>Matrix</p>
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22 <p>
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23 </p>
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24 <h2>SYNOPSIS</h2>
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25 <p>use Matrix;</p>
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26 <p>use Matrix qw(:all);</p>
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27 <p>
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28 </p>
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29 <h2>DESCRIPTION</h2>
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30 <p><strong>Matrix</strong> class provides the following methods:</p>
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31 <p> <a href="#new">new</a>, <a href="#addcolumnvalues">AddColumnValues</a>, <a href="#addrowvalues">AddRowValues</a>, <a href="#copy">Copy</a>, <a href="#getcolumnvalues">GetColumnValues</a>
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32 , <a href="#getcolumnvaluesascolumnmatrix">GetColumnValuesAsColumnMatrix</a>, <a href="#getcolumnvaluesasrowmatrix">GetColumnValuesAsRowMatrix</a>
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33 , <a href="#getcolumnvaluesasstring">GetColumnValuesAsString</a>, <a href="#getcolumnvaluesasvector">GetColumnValuesAsVector</a>, <a href="#getdiagonalvalues">GetDiagonalValues</a>
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34 , <a href="#getdiagonalvaluesascolumnmatrix">GetDiagonalValuesAsColumnMatrix</a>, <a href="#getdiagonalvaluesasrowmatrix">GetDiagonalValuesAsRowMatrix</a>
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35 , <a href="#getdiagonalvaluesasstring">GetDiagonalValuesAsString</a>, <a href="#getdiagonalvaluesasvector">GetDiagonalValuesAsVector</a>, <a href="#getdimension">GetDimension</a>
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36 , <a href="#getmatrixvaluesreference">GetMatrixValuesReference</a>, <a href="#getnumofcolumns">GetNumOfColumns</a>, <a href="#getnumofrows">GetNumOfRows</a>, <a href="#getrowvalues">GetRowValues</a>
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37 , <a href="#getrowvaluesascolumnmatrix">GetRowValuesAsColumnMatrix</a>, <a href="#getrowvaluesasrowmatrix">GetRowValuesAsRowMatrix</a>, <a href="#getrowvaluesasstring">GetRowValuesAsString</a>
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38 , <a href="#getrowvaluesasvector">GetRowValuesAsVector</a>, <a href="#getsize">GetSize</a>, <a href="#getvalue">GetValue</a>, <a href="#identitymatrix">IdentityMatrix</a>, <a href="#isantisymmetric">IsAntiSymmetric</a>
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39 , <a href="#isbidiagonal">IsBiDiagonal</a>, <a href="#isdiagonal">IsDiagonal</a>, <a href="#isidentity">IsIdentity</a>, <a href="#islefttriangular">IsLeftTriangular</a>, <a href="#islowerbidiagonal">IsLowerBiDiagonal</a>
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40 , <a href="#islowertriangular">IsLowerTriangular</a>, <a href="#islowerunitriangular">IsLowerUniTriangular</a>, <a href="#ismatrix">IsMatrix</a>, <a href="#isnegative">IsNegative</a>, <a href="#ispositive">IsPositive</a>
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41 , <a href="#isrighttriangular">IsRightTriangular</a>, <a href="#isskewsymmetric">IsSkewSymmetric</a>, <a href="#issquare">IsSquare</a>, <a href="#isstrictlylowertriangular">IsStrictlyLowerTriangular</a>
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42 , <a href="#isstrictlyuppertriangular">IsStrictlyUpperTriangular</a>, <a href="#issymmetric">IsSymmetric</a>, <a href="#istridiagonal">IsTriDiagonal</a>, <a href="#isunit">IsUnit</a>
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43 , <a href="#isunitlowertriangular">IsUnitLowerTriangular</a>, <a href="#isunituppertriangular">IsUnitUpperTriangular</a>, <a href="#isupperbidiagonal">IsUpperBiDiagonal</a>
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44 , <a href="#isuppertriangular">IsUpperTriangular</a>, <a href="#isupperunitriangular">IsUpperUniTriangular</a>, <a href="#newfromcolumns">NewFromColumns</a>, <a href="#newfromdiagonal">NewFromDiagonal</a>
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45 , <a href="#newfromrows">NewFromRows</a>, <a href="#one">One</a>, <a href="#setallvalues">SetAllValues</a>, <a href="#setcolumnvalues">SetColumnValues</a>, <a href="#setdiagonalvalues">SetDiagonalValues</a>
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46 , <a href="#setmatrixprintstyle">SetMatrixPrintStyle</a>, <a href="#setrowvalues">SetRowValues</a>, <a href="#setvalue">SetValue</a>, <a href="#setvalueprintformat">SetValuePrintFormat</a>, <a href="#stringifymatrix">StringifyMatrix</a>
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47 , <a href="#transpose">Transpose</a>, <a href="#unitmatrix">UnitMatrix</a>, <a href="#zero">Zero</a>, <a href="#zeromatrix">ZeroMatrix</a>
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48 </p><p>The following functions are available:</p>
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49 <p>IsMatrix, IdentityMatrix, NewFromRows, NewFromColumns, NewFromDiagonal,
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50 UnitMatrix, ZeroMatrix</p>
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51 <p>The following operators are overloaded:</p>
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52 <div class="OptionsBox">
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53 "" bool !
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54 <br/> @{}
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55 <br/> + - * / ** %
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56 <br/> == != < <= > >=
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57 <br/> neg
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58 <br/> abs exp log sqrt cos sin</div>
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59 <p>The matrix row and column indicies start from zero.</p>
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60 <p>
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61 </p>
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62 <h2>FUNCTIONS</h2>
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63 <dl>
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64 <dt><strong><a name="new" class="item"><strong>new</strong></a></strong></dt>
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65 <dd>
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66 <div class="OptionsBox">
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67 $NewMatrix = $Matrix->new($NumOfRows, $NumOfCols);</div>
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68 <p>Creates a new <strong>Matrix</strong> of size <em>NumOfRows x NumOfCol</em> and returns <strong>NewMatrix</strong>
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69 object.</p>
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70 </dd>
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71 <dt><strong><a name="addcolumnvalues" class="item"><strong>AddColumnValues</strong></a></strong></dt>
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72 <dd>
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73 <div class="OptionsBox">
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74 $Matrix->AddColumnValues(@Values);
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75 <br/> $Matrix->AddColumnValues(\@Values);
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76 <br/> $Matrix->AddColumnValues($VectorObject);
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77 <br/> $Matrix->AddColumnValues("Value1 Value2 Value3 ...");</div>
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78 <p>Adds column values to <em>Matrix</em> using an array, reference to an array, another vector, or space
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79 delimited value string and returns <em>Matrix</em>.</p>
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80 </dd>
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81 <dt><strong><a name="addrowvalues" class="item"><strong>AddRowValues</strong></a></strong></dt>
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82 <dd>
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83 <div class="OptionsBox">
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84 $Matrix->AddRowValues(@Values);
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85 <br/> $Matrix->AddRowValues(\@Values);
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86 <br/> $Matrix->AddRowValues($VectorObject);
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87 <br/> $Matrix->AddRowValues("Value1 Value2 Value3 ...");</div>
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88 <p>Adds row values to <em>Matrix</em> using an array, reference to an array, another vector, or space
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89 delimited value string and returns <strong>Matrix</strong>.</p>
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90 </dd>
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91 <dt><strong><a name="copy" class="item"><strong>Copy</strong></a></strong></dt>
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92 <dd>
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93 <div class="OptionsBox">
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94 $NewMatrix = $Matrix->Copy();</div>
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95 <p>Creates a copy of <em>Matrix</em> and returns <strong>NewMatrix</strong>.</p>
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96 </dd>
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97 <dt><strong><a name="getcolumnvalues" class="item"><strong>GetColumnValues</strong></a></strong></dt>
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98 <dd>
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99 <div class="OptionsBox">
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100 @Values = $Matrix->GetColumnValues($ColIndex);
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101 <br/> $ValueCount = $Matrix->GetColumnValues($ColIndex);</div>
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102 <p>Returns an array containing column value specified using <em>ColIndex</em> with column index
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103 starting at 0. In scalar context, number of column values is returned.</p>
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104 </dd>
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105 <dt><strong><a name="getcolumnvaluesascolumnmatrix" class="item"><strong>GetColumnValuesAsColumnMatrix</strong></a></strong></dt>
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106 <dd>
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107 <div class="OptionsBox">
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108 $ColumnMatrix = $Matrix->GetColumnValuesAsColumnMatrix($ColIndex);</div>
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109 <p>Returns a new <strong>ColumnMatrix</strong> containing column values specified using <em>ColIndex</em> with
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110 column index starting at 0.</p>
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111 </dd>
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112 <dt><strong><a name="getcolumnvaluesasrowmatrix" class="item"><strong>GetColumnValuesAsRowMatrix</strong></a></strong></dt>
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113 <dd>
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114 <div class="OptionsBox">
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115 $RowMatrix = $Matrix->GetColumnValuesAsRowMatrix($ColIndex);</div>
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116 <p>Returns a new <strong>RowMatrix</strong> containing column values specified using <em>ColIndex</em> with
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117 column index starting at 0.</p>
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118 </dd>
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119 <dt><strong><a name="getcolumnvaluesasstring" class="item"><strong>GetColumnValuesAsString</strong></a></strong></dt>
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120 <dd>
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121 <div class="OptionsBox">
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122 $ColumnValuesString = $Matrix->GetColumnValuesAsString($ColIndex);</div>
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123 <p>Returns a space delimited <strong>ColumnValuesString</strong> column values specified using <em>ColIndex</em> with
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124 column index starting at 0.</p>
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125 </dd>
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126 <dt><strong><a name="getcolumnvaluesasvector" class="item"><strong>GetColumnValuesAsVector</strong></a></strong></dt>
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127 <dd>
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128 <div class="OptionsBox">
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129 $ColumnVector = $Matrix->GetColumnValuesAsVector($ColIndex);</div>
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130 <p>Returns a new <strong>ColumnVector</strong> column values specified using <em>RowIndex</em> with
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131 column index starting at 0.</p>
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132 </dd>
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133 <dt><strong><a name="getdiagonalvalues" class="item"><strong>GetDiagonalValues</strong></a></strong></dt>
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134 <dd>
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135 <div class="OptionsBox">
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136 @Values = $Matrix->GetDiagonalValues();
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137 <br/> $ValueCount = $Matrix->GetDiagonalValues();</div>
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138 <p>Returns an array containing diagonal values. In scalar context, number of diagonal
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139 values is returned.</p>
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140 </dd>
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141 <dt><strong><a name="getdiagonalvaluesascolumnmatrix" class="item"><strong>GetDiagonalValuesAsColumnMatrix</strong></a></strong></dt>
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142 <dd>
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143 <div class="OptionsBox">
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144 $ColumnMatrix = $Matrix->GetDiagonalValuesAsColumnMatrix();</div>
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145 <p>Returns a new <strong>ColumnMatrix</strong> containing diagonal values corresponding to <em>Matrix</em>.</p>
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146 </dd>
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147 <dt><strong><a name="getdiagonalvaluesasrowmatrix" class="item"><strong>GetDiagonalValuesAsRowMatrix</strong></a></strong></dt>
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148 <dd>
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149 <div class="OptionsBox">
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150 $RowMatrix = $Matrix->GetDiagonalValuesAsRowMatrix();</div>
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151 <p>Returns a new <strong>RowMatrix</strong> containing diagonal values corresponding to <em>Matrix</em>.</p>
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152 </dd>
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153 <dt><strong><a name="getdiagonalvaluesasstring" class="item"><strong>GetDiagonalValuesAsString</strong></a></strong></dt>
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154 <dd>
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155 <div class="OptionsBox">
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156 $DiagonalValuesString = $Matrix->GetDiagonalValuesAsString();</div>
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157 <p>Returns a space delimited <strong>DiagonalValuesString</strong> containing diagonal values corresponding to
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158 <em>Matrix</em>.</p>
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159 </dd>
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160 <dt><strong><a name="getdiagonalvaluesasvector" class="item"><strong>GetDiagonalValuesAsVector</strong></a></strong></dt>
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161 <dd>
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162 <div class="OptionsBox">
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163 $DiagonalVector = $Matrix->GetDiagonalValuesAsVector();</div>
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164 <p>Returns a new <strong>DiagonalVector</strong> containing diagonal values corresponding to <em>Matrix</em>.</p>
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165 </dd>
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166 <dt><strong><a name="getdimension" class="item"><strong>GetDimension</strong></a></strong></dt>
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167 <dd>
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168 <div class="OptionsBox">
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169 ($NumOfRows, $NumOfCols) = $Matrix->GetDimension();</div>
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170 <p>Returns size of <em>Matrix</em>.</p>
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171 </dd>
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172 <dt><strong><a name="getmatrixvaluesreference" class="item"><strong>GetMatrixValuesReference</strong></a></strong></dt>
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173 <dd>
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174 <div class="OptionsBox">
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175 $ValuesRef = $Matrix->GetMatrixValuesReference();</div>
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176 <p>Returns a reference to array containing rows and column values corresponding to <em>Matrix</em>.</p>
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177 </dd>
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178 <dt><strong><a name="getnumofcolumns" class="item"><strong>GetNumOfColumns</strong></a></strong></dt>
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179 <dd>
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180 <div class="OptionsBox">
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181 $NumOfCols = $Matrix->GetNumOfColumns();</div>
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182 <p>Returns <strong>NumOfCols</strong> in <em>Matrix</em>.</p>
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183 </dd>
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184 <dt><strong><a name="getnumofrows" class="item"><strong>GetNumOfRows</strong></a></strong></dt>
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185 <dd>
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186 <div class="OptionsBox">
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187 $NumOfRows = $Matrix->GetNumOfRows();</div>
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188 <p>Returns <strong>NumOfRows</strong> in <em>Matrix</em>.</p>
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189 </dd>
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190 <dt><strong><a name="getrowvalues" class="item"><strong>GetRowValues</strong></a></strong></dt>
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191 <dd>
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192 <div class="OptionsBox">
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193 @Values = $Matrix->GetRowValues($RowIndex);
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194 <br/> $ValueCount = $Matrix->GetRowValues($RowIndex);</div>
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195 <p>Returns an array containing row value specified using <em>RowIndex</em> with row index
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196 starting at 0. In scalar context, number of row values is returned.</p>
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197 </dd>
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198 <dt><strong><a name="getrowvaluesascolumnmatrix" class="item"><strong>GetRowValuesAsColumnMatrix</strong></a></strong></dt>
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199 <dd>
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200 <div class="OptionsBox">
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201 $ColumnMatrix = $Matrix->GetRowValuesAsColumnMatrix($RowIndex);</div>
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202 <p>Returns a new <strong>ColumnMatrix</strong> containing row values specified using <em>RowIndex</em> with
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203 column index starting at 0.</p>
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204 </dd>
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205 <dt><strong><a name="getrowvaluesasrowmatrix" class="item"><strong>GetRowValuesAsRowMatrix</strong></a></strong></dt>
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206 <dd>
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207 <div class="OptionsBox">
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208 $RowMatrix = $Matrix->GetRowValuesAsRowMatrix($RowIndex);</div>
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209 <p>Returns a new <strong>RowMatrix</strong> containing row values specified using <em>RowIndex</em> with
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210 row index starting at 0.</p>
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211 </dd>
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212 <dt><strong><a name="getrowvaluesasstring" class="item"><strong>GetRowValuesAsString</strong></a></strong></dt>
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213 <dd>
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214 <div class="OptionsBox">
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215 $RowValuesString = $Matrix->GetRowValuesAsString($RowIndex);</div>
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216 <p>Returns a space delimited <strong>RowValuesString</strong> row values specified using <em>RowIndex</em> with
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217 row index starting at 0.</p>
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218 </dd>
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219 <dt><strong><a name="getrowvaluesasvector" class="item"><strong>GetRowValuesAsVector</strong></a></strong></dt>
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220 <dd>
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221 <div class="OptionsBox">
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222 $RowVector = $Matrix->GetColumnValuesAsVector($RowIndex);</div>
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223 <p>Returns a new <strong>RowVector</strong> row values specified using <em>RowIndex</em> with
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224 row index starting at 0.</p>
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225 </dd>
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226 <dt><strong><a name="getsize" class="item"><strong>GetSize</strong></a></strong></dt>
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227 <dd>
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228 <div class="OptionsBox">
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229 ($NumOfRows, $NumOfCols) = $Matrix->GetSize();</div>
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230 <p>Returns size of <em>Matrix</em>.</p>
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231 </dd>
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232 <dt><strong><a name="getvalue" class="item"><strong>GetValue</strong></a></strong></dt>
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233 <dd>
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234 <div class="OptionsBox">
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235 $Value = $Matrix->GetValue($RowIndex, $ColIndex, [$SkipIndexCheck]);</div>
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236 <p>Returns <strong>Value</strong> of <em>Matrix</em> element specified using <em>RowIndex</em> and <em>ColIndex</em> with indicies
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237 starting at 0 with optional validation of specified index values.</p>
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238 </dd>
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239 <dt><strong><a name="identitymatrix" class="item"><strong>IdentityMatrix</strong></a></strong></dt>
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240 <dd>
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241 <div class="OptionsBox">
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242 $NewIdentityMatrix = $Matrix->IdentityMatrix($NumOfRows, $NumOfCols);
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243 <br/> $NewIdentityMatrix = Matrix::IdentityMatrix($NumOfRows, $NumOfCols);
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244 <br/> $NewIdentityMatrix = Matrix::IdentityMatrix();</div>
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245 <p>Creates a new <strong>IdentityMatrix</strong> of specified size <em>NumOfRows x NumOfCol</em> or of size 3 x 3 and
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246 returns <strong>NewIdentityMatrix</strong> object.</p>
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247 </dd>
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248 <dt><strong><a name="isantisymmetric" class="item"><strong>IsAntiSymmetric</strong></a></strong></dt>
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249 <dd>
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250 <div class="OptionsBox">
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251 $Status = $Matrix->IsAntiSymmetric();</div>
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252 <p>Returns 1 or 0 based on whether <em>Matrix</em> is an anti symmetric matrix.</p>
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253 <p>A matrix is an anti symmetric matrix:</p>
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254 <div class="OptionsBox">
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255 . It's a square matrix
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256 <br/> . Its elements are asymmetric with respect to main diagonal. In other words,
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257 elements below the main diagonal are equal to the negative of elements above
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258 the main diagonal.</div>
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259 <p>Transpose of an anti symmetric matrix equals the negative of the matrix.</p>
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260 </dd>
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261 <dt><strong><a name="isbidiagonal" class="item"><strong>IsBiDiagonal</strong></a></strong></dt>
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262 <dd>
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263 <div class="OptionsBox">
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264 $Status = $Matrix->IsBiDiagonal();</div>
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265 <p>Returns 1 or 0 based on whether <em>Matrix</em> is upper or lower bidiagonal matrix.</p>
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266 </dd>
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267 <dt><strong><a name="isdiagonal" class="item"><strong>IsDiagonal</strong></a></strong></dt>
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268 <dd>
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269 <div class="OptionsBox">
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270 $Status = $Matrix->IsDiagonal();</div>
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271 <p>Returns 1 or 0 based on whether <em>Matrix</em> is a diagonal matrix.</p>
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272 <p>A matrix is a diagonal matrix:</p>
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273 <div class="OptionsBox">
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274 . It's a square matrix
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275 <br/> . All its off-diagonal elements are zeros and its diagonal elements may or may not
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276 be zeros</div>
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277 </dd>
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278 <dt><strong><a name="isidentity" class="item"><strong>IsIdentity</strong></a></strong></dt>
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279 <dd>
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280 <div class="OptionsBox">
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281 $Status = $Matrix->IsIdentity();</div>
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282 <p>Returns 1 or 0 based on whether <em>Matrix</em> is an identity matrix.</p>
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283 </dd>
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284 <dt><strong><a name="islefttriangular" class="item"><strong>IsLeftTriangular</strong></a></strong></dt>
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285 <dd>
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286 <div class="OptionsBox">
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287 $Status = $Matrix->IsLeftTriangular();</div>
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288 <p>Returns 1 or 0 based on whether <em>Matrix</em> is a left or lower matrix.</p>
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289 <p>A matrix is a left triangular matrix:</p>
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290 <div class="OptionsBox">
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291 . It's a square matrix
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292 <br/> . All its entries above the main diagonal are zero</div>
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293 </dd>
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294 <dt><strong><a name="islowerbidiagonal" class="item"><strong>IsLowerBiDiagonal</strong></a></strong></dt>
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295 <dd>
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296 <div class="OptionsBox">
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297 $Status = $Matrix->IsLowerBiDiagonal();</div>
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298 <p>Returns 1 or 0 based on whether <em>Matrix</em> is a lower bidiagonal matrix.</p>
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299 <p>A matrix is a lower bidiagonal matrix:</p>
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300 <div class="OptionsBox">
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301 . It's a square matrix
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302 <br/> . All its main diagonal and lower diagonal elements are non-zeros and all its
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303 other elements are zeros</div>
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304 </dd>
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305 <dt><strong><a name="islowertriangular" class="item"><strong>IsLowerTriangular</strong></a></strong></dt>
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306 <dd>
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307 <div class="OptionsBox">
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308 $Status = $Matrix->IsLowerTriangular();</div>
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309 <p>Returns 1 or 0 based on whether <em>Matrix</em> is a left or lower triangular matrix.</p>
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310 <p>A matrix is a lower triangular matrix:</p>
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311 <div class="OptionsBox">
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312 . It's a square matrix
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313 <br/> . All its entries above the main diagonal are zero</div>
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314 </dd>
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315 <dt><strong><a name="islowerunitriangular" class="item"><strong>IsLowerUniTriangular</strong></a></strong></dt>
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316 <dd>
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317 <div class="OptionsBox">
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318 $Status = $Matrix->IsLowerUniTriangular();</div>
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319 <p>Returns 1 or 0 based on whether <em>Matrix</em> is a lower triangular matrix.</p>
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320 </dd>
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321 <dt><strong><a name="ismatrix" class="item"><strong>IsMatrix</strong></a></strong></dt>
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322 <dd>
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323 <div class="OptionsBox">
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324 $Status = Matrix::IsMatrix($Object);</div>
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325 <p>Returns 1 or 0 based on whether <em>Object</em> is a <strong>Matrix</strong> object.</p>
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326 </dd>
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327 <dt><strong><a name="isnegative" class="item"><strong>IsNegative</strong></a></strong></dt>
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328 <dd>
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329 <div class="OptionsBox">
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330 $Status = $Matrix->IsNegative();</div>
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331 <p>Returns 1 or 0 based on whether <em>Matrix</em> is a negative matrix containing only values
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332 less than or equal to zero.</p>
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333 </dd>
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334 <dt><strong><a name="ispositive" class="item"><strong>IsPositive</strong></a></strong></dt>
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335 <dd>
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336 <div class="OptionsBox">
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337 $Status = $Matrix->IsPositive();</div>
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338 <p>Returns 1 or 0 based on whether <em>Matrix</em> is a negative matrix containing only values
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339 greater than or equal to zero.</p>
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340 </dd>
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341 <dt><strong><a name="isrighttriangular" class="item"><strong>IsRightTriangular</strong></a></strong></dt>
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342 <dd>
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343 <div class="OptionsBox">
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344 $Status = $Matrix->IsRightTriangular();</div>
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345 <p>Returns 1 or 0 based on whether <em>Matrix</em> is a right or upper triangular matrix.</p>
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346 </dd>
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347 <dt><strong><a name="isskewsymmetric" class="item"><strong>IsSkewSymmetric</strong></a></strong></dt>
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348 <dd>
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349 <div class="OptionsBox">
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350 $Status = $Matrix->IsSkewSymmetric();</div>
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351 <p>Returns 1 or 0 based on whether <em>Matrix</em> is a skew or anti symmetric matrix.</p>
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352 </dd>
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353 <dt><strong><a name="issquare" class="item"><strong>IsSquare</strong></a></strong></dt>
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354 <dd>
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355 <div class="OptionsBox">
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356 $Status = $Matrix->IsSquare();</div>
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357 <p>Returns 1 or 0 based on whether <em>Matrix</em> is a square matrix containing equal
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358 number of rows and columns.</p>
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359 </dd>
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360 <dt><strong><a name="isstrictlylowertriangular" class="item"><strong>IsStrictlyLowerTriangular</strong></a></strong></dt>
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361 <dd>
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362 <div class="OptionsBox">
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363 $Status = $Matrix->IsStrictlyLowerTriangular();</div>
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364 <p>Returns 1 or 0 based on whether <em>Matrix</em> is a strictly lower triangular matrix.</p>
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365 <p>A matrix is a strictly lower triangular matrix:</p>
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366 <div class="OptionsBox">
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367 . It's a square matrix
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368 <br/> . All its entries on and above the main diagonal are zero</div>
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369 </dd>
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370 <dt><strong><a name="isstrictlyuppertriangular" class="item"><strong>IsStrictlyUpperTriangular</strong></a></strong></dt>
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371 <dd>
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372 <div class="OptionsBox">
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373 $Status = $Matrix->IsStrictlyUpperTriangular();</div>
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374 <p>Returns 1 or 0 based on whether <em>Matrix</em> is a strictly upper triangular matrix.</p>
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375 <p>A matrix is a strictly upper triangular matrix:</p>
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376 <div class="OptionsBox">
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377 . It's a square matrix
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378 <br/> . All its entries on and below the main diagonal are zero</div>
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379 </dd>
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380 <dt><strong><a name="issymmetric" class="item"><strong>IsSymmetric</strong></a></strong></dt>
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381 <dd>
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382 <div class="OptionsBox">
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383 $Status = $Matrix->IsSymmetric();</div>
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384 <p>Returns 1 or 0 based on whether <em>Matrix</em> is a symmetric matrix.</p>
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385 <p>A matrix is a symmetric matrix:</p>
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386 <div class="OptionsBox">
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387 . It's a square matrix
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388 <br/> . Its elements are symmetric with respect to main diagonal. In other words,
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389 elements below the main diagonal are equal to the elements above the main
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390 diagonal.</div>
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391 <p>Transpose of a symmetric matrix equals the matrix itself.</p>
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392 </dd>
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393 <dt><strong><a name="istridiagonal" class="item"><strong>IsTriDiagonal</strong></a></strong></dt>
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394 <dd>
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395 <div class="OptionsBox">
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396 $Status = $Matrix->IsTriDiagonal();</div>
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397 <p>Returns 1 or 0 based on whether <em>Matrix</em> is a tridiagonal matrix.</p>
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398 <p>A matrix is a tribidiagonal matrix:</p>
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399 <div class="OptionsBox">
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400 . It's a square matrix
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401 <br/> . All its main diagonal, upper diagonal, and lower diagonal elements are non-zeros and all its
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402 other elements are zeros</div>
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403 </dd>
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404 <dt><strong><a name="isunit" class="item"><strong>IsUnit</strong></a></strong></dt>
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405 <dd>
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406 <div class="OptionsBox">
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407 $Status = $Matrix->IsUnit();</div>
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408 <p>Returns 1 or 0 based on whether <em>Matrix</em> is a unit matrix.</p>
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409 <p>A matrix is a unit matrix:</p>
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410 <div class="OptionsBox">
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411 . It's a square matrix
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412 <br/> . All its diagonal elements are ones and its off-diagonal elements are zeros</div>
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413 </dd>
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414 <dt><strong><a name="isunitlowertriangular" class="item"><strong>IsUnitLowerTriangular</strong></a></strong></dt>
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415 <dd>
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416 <div class="OptionsBox">
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417 $Status = $Matrix->IsUnitLowerTriangular();</div>
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418 <p>Returns 1 or 0 based on whether <em>Matrix</em> is an unit lower triangular matrix.</p>
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419 <p>A matrix is an unit lower triangular matrix:</p>
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420 <div class="OptionsBox">
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421 . It's a square matrix
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422 <br/> . All its entries main diagonal are one
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423 <br/> . All its entries above the main diagonal are zero</div>
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424 </dd>
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425 <dt><strong><a name="isunituppertriangular" class="item"><strong>IsUnitUpperTriangular</strong></a></strong></dt>
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426 <dd>
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427 <div class="OptionsBox">
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428 $Status = $Matrix->IsUnitUpperTriangular();</div>
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429 <p>Returns 1 or 0 based on whether <em>Matrix</em> is an unit upper triangular matrix.</p>
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430 <p>A matrix is an unit upper triangular matrix:</p>
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431 <div class="OptionsBox">
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432 . It's a square matrix
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433 <br/> . All its entries main diagonal are one
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434 <br/> . All its entries below the main diagonal are zero</div>
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435 </dd>
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436 <dt><strong><a name="isupperbidiagonal" class="item"><strong>IsUpperBiDiagonal</strong></a></strong></dt>
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437 <dd>
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438 <div class="OptionsBox">
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439 $Status = $Matrix->IsUpperBiDiagonal();</div>
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440 <p>Returns 1 or 0 based on whether <em>Matrix</em> is an upper bidiagonal matrix.</p>
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441 <p>A matrix is an upper bidiagonal matrix:</p>
|
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442 <div class="OptionsBox">
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443 . It's a square matrix
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444 <br/> . All its main diagonal and upper diagonal elements are non-zeros and all its
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445 other elements are zeros</div>
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446 </dd>
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447 <dt><strong><a name="isuppertriangular" class="item"><strong>IsUpperTriangular</strong></a></strong></dt>
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448 <dd>
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449 <div class="OptionsBox">
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450 $Status = $Matrix->IsUpperTriangular();</div>
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451 <p>Returns 1 or 0 based on whether <em>Matrix</em> is a right or upper triangular matrix.</p>
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452 <p>A matrix is an upper triangular matrix:</p>
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453 <div class="OptionsBox">
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454 . It's a square matrix
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455 <br/> . All its entries below the main diagonal are zero</div>
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456 </dd>
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457 <dt><strong><a name="isupperunitriangular" class="item"><strong>IsUpperUniTriangular</strong></a></strong></dt>
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458 <dd>
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459 <div class="OptionsBox">
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460 $Status = $Matrix->IsUpperUniTriangular();</div>
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461 <p>Returns 1 or 0 based on whether <em>Matrix</em> is a right or upper triangular matrix.</p>
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462 </dd>
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463 <dt><strong><a name="newfromcolumns" class="item"><strong>NewFromColumns</strong></a></strong></dt>
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464 <dd>
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465 <div class="OptionsBox">
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466 $NewMatrix = Matrix::NewFromColumns($Col1Vector, $Col2Vector, ...);
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467 <br/> $NewMatrix = Matrix::NewFromColumns($Col1ValuesRef, $Col2ValuesRef, ...);
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468 <br/> $NewMatrix = Matrix::NewFromColumns("Val1 Val2 ...", "Val1 Val2", ...);</div>
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469 <div class="OptionsBox">
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470 $NewMatrix = $Matrix->NewFromColumns($Col1Vector, $Col2Vector, ...);
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471 <br/> $NewMatrix = $Matrix->NewFromColumns($Col1ValuesRef, $Col2ValuesRef, ...);
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472 <br/> $NewMatrix = $Matrix->NewFromColumns("Val1 Val2 ...", "Val1 Val2", ...);</div>
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473 <p>Creates a new <strong>Matrix</strong> using specified column values and returns <strong>NewMatrix</strong> object.</p>
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474 <p>The column values can be specified in one of the following formats:</p>
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475 <div class="OptionsBox">
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476 . List of vector objects
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477 <br/> . References to list of values
|
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478 <br/> . List of strings containing columns values delimited by space</div>
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479 <p>Each column must contain the same number of values.</p>
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480 </dd>
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481 <dt><strong><a name="newfromdiagonal" class="item"><strong>NewFromDiagonal</strong></a></strong></dt>
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482 <dd>
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483 <div class="OptionsBox">
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484 $NewMatrix = Matrix::NewFromDiagonal($DiagonalVector);
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485 <br/> $NewMatrix = Matrix::NewFromDiagonal($DiagonalValuesRef);
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486 <br/> $NewMatrix = Matrix::NewFromDiagonal("Val1 Val2 ...");</div>
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487 <div class="OptionsBox">
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488 $NewMatrix = Matrix->NewFromDiagonal($DiagonalVector);
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489 <br/> $NewMatrix = Matrix->NewFromDiagonal($DiagonalValuesRef);
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490 <br/> $NewMatrix = Matrix->NewFromDiagonal("Val1 Val2 ...");</div>
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|
491 <p>Creates a new <strong>Matrix</strong> using specified diagonal values and returns <strong>NewMatrix</strong> object.</p>
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492 <p>The column values can be specified in one of the following formats:</p>
|
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|
493 <div class="OptionsBox">
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494 . A vector object
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|
495 <br/> . Reference to list of values
|
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|
496 <br/> . Strings containing diagonal values delimited by space</div>
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497 </dd>
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498 <dt><strong><a name="newfromrows" class="item"><strong>NewFromRows</strong></a></strong></dt>
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499 <dd>
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500 <div class="OptionsBox">
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501 $NewMatrix = Matrix::NewFromRows($Row1Vector, $RowVector, ...);
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502 <br/> $NewMatrix = Matrix::NewFromRows($Row1ValuesRef, $Row2ValuesRef, ...);
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503 <br/> $NewMatrix = Matrix::NewFromRows("Val1 Val2 ...", "Val1 Val2", ...);</div>
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|
504 <div class="OptionsBox">
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505 $NewMatrix = $Matrix->NewFromRows($Row1Vector, $Row2Vector, ...);
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|
506 <br/> $NewMatrix = $Matrix->NewFromRows($Row1ValuesRef, $Row2ValuesRef, ...);
|
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|
507 <br/> $NewMatrix = $Matrix->NewFromRows("Val1 Val2 ...", "Val1 Val2", ...);</div>
|
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|
508 <p>Creates a new <strong>Matrix</strong> using specified row values and returns <strong>NewMatrix</strong> object.</p>
|
|
|
509 <p>The row values can be specified in one of the following formats:</p>
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|
510 <div class="OptionsBox">
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|
511 . List of vector objects
|
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|
512 <br/> . References to list of values
|
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513 <br/> . List of strings containing columns values delimited by space</div>
|
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|
514 <p>Each row must contain the same number of values.</p>
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515 </dd>
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516 <dt><strong><a name="one" class="item"><strong>One</strong></a></strong></dt>
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517 <dd>
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518 <div class="OptionsBox">
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519 $Matrix->One();</div>
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520 <p>Sets values of all <em>Matrix</em> elements to 1 and returns <em>Matrix</em>.</p>
|
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|
521 </dd>
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522 <dt><strong><a name="setallvalues" class="item"><strong>SetAllValues</strong></a></strong></dt>
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523 <dd>
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524 <div class="OptionsBox">
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525 $Matrix->SetAllValues($Value);</div>
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526 <p>Sets values of all <em>Matrix</em> elements to specified <em>Value</em> and returns <em>Matrix</em>.</p>
|
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|
527 </dd>
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528 <dt><strong><a name="setcolumnvalues" class="item"><strong>SetColumnValues</strong></a></strong></dt>
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529 <dd>
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530 <div class="OptionsBox">
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531 $Matrix->SetColumnValues($ColIndex, @Values);
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532 <br/> $Matrix->SetColumnValues($ColIndex, \@Values);
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533 <br/> $Matrix->SetColumnValues($ColIndex, $VectorObject);
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534 <br/> $Matrix->SetColumnValues($ColIndex, "Value1 Value2 Value3 ...");</div>
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|
535 <p>Sets column values of a specified <em>ColIndex</em> of <em>Matrix</em> using an array, reference to an array,
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|
536 another vector, or space delimited value string and returns <em>Matrix</em>.</p>
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|
537 </dd>
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538 <dt><strong><a name="setdiagonalvalues" class="item"><strong>SetDiagonalValues</strong></a></strong></dt>
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539 <dd>
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540 <div class="OptionsBox">
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|
541 $Matrix->SetDiagonalValues(@Values);
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542 <br/> $Matrix->SetDiagonalValues(\@Values);
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|
543 <br/> $Matrix->SetDiagonalValues($VectorObject);
|
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|
544 <br/> $Matrix->SetDiagonalValues("Value1 Value2 Value3 ...");</div>
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|
545 <p>Sets values of the diagonal in square <em>Matrix</em> and returns <em>Matrix</em>.</p>
|
|
|
546 </dd>
|
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|
547 <dt><strong><a name="setmatrixprintstyle" class="item"><strong>SetMatrixPrintStyle</strong></a></strong></dt>
|
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|
548 <dd>
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|
549 <div class="OptionsBox">
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|
550 $Matrix->SetMatrixPrintStyle($MatrixStyle);
|
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|
551 <br/> $Matrix::SetMatrixPrintStyle($MatrixStyle);</div>
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|
552 <p>Sets print style for matrix rows for an individual object or the whole class during StringifyMatrix
|
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|
553 operation. Possible <em>MatrixStyle</em> values: <em>AllRowsInOneLine, OneRowPerLine</em>. Default:
|
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|
554 <em>AllRowsInOneLine</em>.</p>
|
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|
555 </dd>
|
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556 <dt><strong><a name="setrowvalues" class="item"><strong>SetRowValues</strong></a></strong></dt>
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557 <dd>
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558 <div class="OptionsBox">
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559 $Matrix->SetRowValues($ColIndex, @Values);
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|
560 <br/> $Matrix->SetRowValues($ColIndex, \@Values);
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561 <br/> $Matrix->SetRowValues($ColIndex, $VectorObjext);
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|
562 <br/> $Matrix->SetRowValues($ColIndex, "Value1 Value2 Value3 ...");</div>
|
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|
563 <p>Sets row values of a specified <em>RowIndex</em> of <em>Matrix</em> using an array, reference to an array,
|
|
|
564 another vector, or space delimited value string and returns <em>Matrix</em>.</p>
|
|
|
565 </dd>
|
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|
566 <dt><strong><a name="setvalue" class="item"><strong>SetValue</strong></a></strong></dt>
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|
567 <dd>
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|
568 <div class="OptionsBox">
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|
569 $Matrix->SetValue($RowIndex, $ColIndex, $Value, [$SkipIndexCheck]);</div>
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|
570 <p>Sets <strong>Value</strong> of <em>Matrix</em> element specified using <em>RowIndex</em> and <em>ColIndex</em> with indicies
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|
571 starting at 0 with optional validation of specified index values and return <em>Matrix</em>.</p>
|
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572 </dd>
|
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|
573 <dt><strong><a name="setvalueprintformat" class="item"><strong>SetValuePrintFormat</strong></a></strong></dt>
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574 <dd>
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575 <div class="OptionsBox">
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576 $Matrix->SetValuePrintFormat($ValueFormat);
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577 <br/> $Matrix::SetValuePrintFormat($ValueFormat);</div>
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|
578 <p>Sets value print format for an individual object or the whole class during StringifyMatrix operation
|
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|
579 and returns <em>Matrix</em>.</p>
|
|
|
580 </dd>
|
|
|
581 <dt><strong><a name="stringifymatrix" class="item"><strong>StringifyMatrix</strong></a></strong></dt>
|
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|
582 <dd>
|
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|
583 <div class="OptionsBox">
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|
584 $String = $Matrix->StringifyMatrix();</div>
|
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|
585 <p>Returns a string containing information about <em>Matrix</em> object.</p>
|
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|
586 </dd>
|
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587 <dt><strong><a name="transpose" class="item"><strong>Transpose</strong></a></strong></dt>
|
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|
588 <dd>
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589 <div class="OptionsBox">
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590 $Matrix->Transpose();</div>
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591 <p>Transposes <em>Matrix</em> by swaping rows with columns and returns <em>Matrix</em>.</p>
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592 </dd>
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593 <dt><strong><a name="unitmatrix" class="item"><strong>UnitMatrix</strong></a></strong></dt>
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594 <dd>
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595 <div class="OptionsBox">
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596 $NewUnitMatrix = $Matrix::UnitMatrix($NumOfRows, $NumOfCols);
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597 <br/> $NewUnitMatrix = $Matrix::UnitMatrix();
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598 <br/> $NewUnitMatrix = $Matrix->UnitMatrix($NumOfRows, $NumOfCols);</div>
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599 <p>Creates a new <strong>UnitMatrix</strong> of specified size <em>NumOfRows x NumOfCol</em> or of size 3 x 3 and
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600 returns <strong>NewUnitMatrix</strong> object.</p>
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601 </dd>
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602 <dt><strong><a name="zero" class="item"><strong>Zero</strong></a></strong></dt>
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603 <dd>
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604 <div class="OptionsBox">
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605 $Matrix->Zero();</div>
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606 <p>Sets values of all <em>Matrix</em> elements to 0 and returns <em>Matrix</em>.</p>
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607 </dd>
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608 <dt><strong><a name="zeromatrix" class="item"><strong>ZeroMatrix</strong></a></strong></dt>
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609 <dd>
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610 <div class="OptionsBox">
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611 $NewZeroMatrix = $Matrix::ZeroMatrix($NumOfRows, $NumOfCols);
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612 <br/> $NewZeroMatrix = $Matrix::ZeroMatrix();
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613 <br/> $NewZeroMatrix = $Matrix->ZeroMatrix($NumOfRows, $NumOfCols);</div>
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614 <p>Creates a new <strong>ZeroMatrix</strong> of specified size <em>NumOfRows x NumOfCol</em> or of size 3 x 3 and
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615 returns <strong>NewZeroMatrix</strong> object.</p>
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616 </dd>
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617 </dl>
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618 <p>
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619 </p>
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620 <h2>AUTHOR</h2>
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621 <p><a href="mailto:msud@san.rr.com">Manish Sud</a></p>
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622 <p>
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623 </p>
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624 <h2>SEE ALSO</h2>
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625 <p><a href="./Vector.html">Vector.pm</a>
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626 </p>
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627 <p>
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628 </p>
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629 <h2>COPYRIGHT</h2>
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630 <p>Copyright (C) 2015 Manish Sud. All rights reserved.</p>
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631 <p>This file is part of MayaChemTools.</p>
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632 <p>MayaChemTools is free software; you can redistribute it and/or modify it under
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633 the terms of the GNU Lesser General Public License as published by the Free
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634 Software Foundation; either version 3 of the License, or (at your option)
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635 any later version.</p>
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636 <p> </p><p> </p><div class="DocNav">
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637 <table width="100%" border=0 cellpadding=0 cellspacing=2>
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638 <tr align="left" valign="top"><td width="33%" align="left"><a href="./MathUtil.html" title="MathUtil.html">Previous</a> <a href="./index.html" title="Table of Contents">TOC</a> <a href="./AtomsCountDescriptors.html" title="AtomsCountDescriptors.html">Next</a></td><td width="34%" align="middle"><strong>March 29, 2015</strong></td><td width="33%" align="right"><strong>Matrix.pm</strong></td></tr>
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639 </table>
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640 </div>
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641 <br />
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642 <center>
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643 <img src="../../images/h2o2.png">
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644 </center>
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645 </body>
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646 </html>
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