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1 NAME
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2 Matrix
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3
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4 SYNOPSIS
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5 use Matrix;
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6
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7 use Matrix qw(:all);
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8
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9 DESCRIPTION
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10 Matrix class provides the following methods:
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11
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12 new, AddColumnValues, AddRowValues, Copy, GetColumnValues,
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13 GetColumnValuesAsColumnMatrix, GetColumnValuesAsRowMatrix,
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14 GetColumnValuesAsString, GetColumnValuesAsVector, GetDiagonalValues,
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15 GetDiagonalValuesAsColumnMatrix, GetDiagonalValuesAsRowMatrix,
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16 GetDiagonalValuesAsString, GetDiagonalValuesAsVector, GetDimension,
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17 GetMatrixValuesReference, GetNumOfColumns, GetNumOfRows, GetRowValues,
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18 GetRowValuesAsColumnMatrix, GetRowValuesAsRowMatrix,
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19 GetRowValuesAsString, GetRowValuesAsVector, GetSize, GetValue,
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20 IdentityMatrix, IsAntiSymmetric, IsBiDiagonal, IsDiagonal, IsIdentity,
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21 IsLeftTriangular, IsLowerBiDiagonal, IsLowerTriangular,
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22 IsLowerUniTriangular, IsMatrix, IsNegative, IsPositive,
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23 IsRightTriangular, IsSkewSymmetric, IsSquare, IsStrictlyLowerTriangular,
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24 IsStrictlyUpperTriangular, IsSymmetric, IsTriDiagonal, IsUnit,
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25 IsUnitLowerTriangular, IsUnitUpperTriangular, IsUpperBiDiagonal,
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26 IsUpperTriangular, IsUpperUniTriangular, NewFromColumns,
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27 NewFromDiagonal, NewFromRows, One, SetAllValues, SetColumnValues,
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28 SetDiagonalValues, SetMatrixPrintStyle, SetRowValues, SetValue,
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29 SetValuePrintFormat, StringifyMatrix, Transpose, UnitMatrix, Zero,
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30 ZeroMatrix
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31
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32 The following functions are available:
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33
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34 IsMatrix, IdentityMatrix, NewFromRows, NewFromColumns, NewFromDiagonal,
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35 UnitMatrix, ZeroMatrix
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36
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37 The following operators are overloaded:
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38
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39 "" bool !
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40 @{}
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41 + - * / ** %
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42 == != < <= > >=
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43 neg
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44 abs exp log sqrt cos sin
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45
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46 The matrix row and column indicies start from zero.
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47
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48 FUNCTIONS
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49 new
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50 $NewMatrix = $Matrix->new($NumOfRows, $NumOfCols);
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51
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52 Creates a new Matrix of size *NumOfRows x NumOfCol* and returns
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53 NewMatrix object.
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54
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55 AddColumnValues
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56 $Matrix->AddColumnValues(@Values);
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57 $Matrix->AddColumnValues(\@Values);
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58 $Matrix->AddColumnValues($VectorObject);
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59 $Matrix->AddColumnValues("Value1 Value2 Value3 ...");
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60
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61 Adds column values to *Matrix* using an array, reference to an
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62 array, another vector, or space delimited value string and returns
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63 *Matrix*.
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64
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65 AddRowValues
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66 $Matrix->AddRowValues(@Values);
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67 $Matrix->AddRowValues(\@Values);
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68 $Matrix->AddRowValues($VectorObject);
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69 $Matrix->AddRowValues("Value1 Value2 Value3 ...");
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70
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71 Adds row values to *Matrix* using an array, reference to an array,
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72 another vector, or space delimited value string and returns Matrix.
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73
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74 Copy
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75 $NewMatrix = $Matrix->Copy();
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76
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77 Creates a copy of *Matrix* and returns NewMatrix.
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78
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79 GetColumnValues
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80 @Values = $Matrix->GetColumnValues($ColIndex);
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81 $ValueCount = $Matrix->GetColumnValues($ColIndex);
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82
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83 Returns an array containing column value specified using *ColIndex*
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84 with column index starting at 0. In scalar context, number of column
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85 values is returned.
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86
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87 GetColumnValuesAsColumnMatrix
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88 $ColumnMatrix = $Matrix->GetColumnValuesAsColumnMatrix($ColIndex);
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89
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90 Returns a new ColumnMatrix containing column values specified using
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91 *ColIndex* with column index starting at 0.
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92
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93 GetColumnValuesAsRowMatrix
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94 $RowMatrix = $Matrix->GetColumnValuesAsRowMatrix($ColIndex);
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95
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96 Returns a new RowMatrix containing column values specified using
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97 *ColIndex* with column index starting at 0.
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98
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99 GetColumnValuesAsString
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100 $ColumnValuesString = $Matrix->GetColumnValuesAsString($ColIndex);
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101
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102 Returns a space delimited ColumnValuesString column values specified
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103 using *ColIndex* with column index starting at 0.
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104
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105 GetColumnValuesAsVector
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106 $ColumnVector = $Matrix->GetColumnValuesAsVector($ColIndex);
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107
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108 Returns a new ColumnVector column values specified using *RowIndex*
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109 with column index starting at 0.
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110
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111 GetDiagonalValues
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112 @Values = $Matrix->GetDiagonalValues();
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113 $ValueCount = $Matrix->GetDiagonalValues();
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114
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115 Returns an array containing diagonal values. In scalar context,
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116 number of diagonal values is returned.
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117
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118 GetDiagonalValuesAsColumnMatrix
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119 $ColumnMatrix = $Matrix->GetDiagonalValuesAsColumnMatrix();
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120
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121 Returns a new ColumnMatrix containing diagonal values corresponding
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122 to *Matrix*.
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123
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124 GetDiagonalValuesAsRowMatrix
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125 $RowMatrix = $Matrix->GetDiagonalValuesAsRowMatrix();
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126
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127 Returns a new RowMatrix containing diagonal values corresponding to
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128 *Matrix*.
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129
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130 GetDiagonalValuesAsString
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131 $DiagonalValuesString = $Matrix->GetDiagonalValuesAsString();
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132
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133 Returns a space delimited DiagonalValuesString containing diagonal
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134 values corresponding to *Matrix*.
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135
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136 GetDiagonalValuesAsVector
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137 $DiagonalVector = $Matrix->GetDiagonalValuesAsVector();
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138
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139 Returns a new DiagonalVector containing diagonal values
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140 corresponding to *Matrix*.
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141
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142 GetDimension
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143 ($NumOfRows, $NumOfCols) = $Matrix->GetDimension();
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144
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145 Returns size of *Matrix*.
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146
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147 GetMatrixValuesReference
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148 $ValuesRef = $Matrix->GetMatrixValuesReference();
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149
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150 Returns a reference to array containing rows and column values
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151 corresponding to *Matrix*.
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152
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153 GetNumOfColumns
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154 $NumOfCols = $Matrix->GetNumOfColumns();
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155
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156 Returns NumOfCols in *Matrix*.
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157
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158 GetNumOfRows
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159 $NumOfRows = $Matrix->GetNumOfRows();
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160
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161 Returns NumOfRows in *Matrix*.
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162
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163 GetRowValues
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164 @Values = $Matrix->GetRowValues($RowIndex);
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165 $ValueCount = $Matrix->GetRowValues($RowIndex);
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166
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167 Returns an array containing row value specified using *RowIndex*
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168 with row index starting at 0. In scalar context, number of row
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169 values is returned.
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170
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171 GetRowValuesAsColumnMatrix
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172 $ColumnMatrix = $Matrix->GetRowValuesAsColumnMatrix($RowIndex);
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173
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174 Returns a new ColumnMatrix containing row values specified using
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175 *RowIndex* with column index starting at 0.
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176
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177 GetRowValuesAsRowMatrix
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178 $RowMatrix = $Matrix->GetRowValuesAsRowMatrix($RowIndex);
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179
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180 Returns a new RowMatrix containing row values specified using
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181 *RowIndex* with row index starting at 0.
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182
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183 GetRowValuesAsString
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184 $RowValuesString = $Matrix->GetRowValuesAsString($RowIndex);
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185
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186 Returns a space delimited RowValuesString row values specified using
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187 *RowIndex* with row index starting at 0.
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188
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189 GetRowValuesAsVector
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190 $RowVector = $Matrix->GetColumnValuesAsVector($RowIndex);
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191
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192 Returns a new RowVector row values specified using *RowIndex* with
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193 row index starting at 0.
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194
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195 GetSize
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196 ($NumOfRows, $NumOfCols) = $Matrix->GetSize();
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197
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198 Returns size of *Matrix*.
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199
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200 GetValue
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201 $Value = $Matrix->GetValue($RowIndex, $ColIndex, [$SkipIndexCheck]);
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202
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203 Returns Value of *Matrix* element specified using *RowIndex* and
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204 *ColIndex* with indicies starting at 0 with optional validation of
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205 specified index values.
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206
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207 IdentityMatrix
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208 $NewIdentityMatrix = $Matrix->IdentityMatrix($NumOfRows, $NumOfCols);
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209 $NewIdentityMatrix = Matrix::IdentityMatrix($NumOfRows, $NumOfCols);
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210 $NewIdentityMatrix = Matrix::IdentityMatrix();
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211
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212 Creates a new IdentityMatrix of specified size *NumOfRows x
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213 NumOfCol* or of size 3 x 3 and returns NewIdentityMatrix object.
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214
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215 IsAntiSymmetric
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216 $Status = $Matrix->IsAntiSymmetric();
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217
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218 Returns 1 or 0 based on whether *Matrix* is an anti symmetric
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219 matrix.
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220
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221 A matrix is an anti symmetric matrix:
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222
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223 . It's a square matrix
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224 . Its elements are asymmetric with respect to main diagonal. In other words,
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225 elements below the main diagonal are equal to the negative of elements above
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226 the main diagonal.
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227
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228 Transpose of an anti symmetric matrix equals the negative of the
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229 matrix.
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230
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231 IsBiDiagonal
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232 $Status = $Matrix->IsBiDiagonal();
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233
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234 Returns 1 or 0 based on whether *Matrix* is upper or lower
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235 bidiagonal matrix.
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236
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237 IsDiagonal
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238 $Status = $Matrix->IsDiagonal();
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239
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240 Returns 1 or 0 based on whether *Matrix* is a diagonal matrix.
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241
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242 A matrix is a diagonal matrix:
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243
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244 . It's a square matrix
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245 . All its off-diagonal elements are zeros and its diagonal elements may or may not
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246 be zeros
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247
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248 IsIdentity
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249 $Status = $Matrix->IsIdentity();
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250
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251 Returns 1 or 0 based on whether *Matrix* is an identity matrix.
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252
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253 IsLeftTriangular
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254 $Status = $Matrix->IsLeftTriangular();
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255
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256 Returns 1 or 0 based on whether *Matrix* is a left or lower matrix.
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257
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258 A matrix is a left triangular matrix:
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259
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260 . It's a square matrix
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261 . All its entries above the main diagonal are zero
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262
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263 IsLowerBiDiagonal
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264 $Status = $Matrix->IsLowerBiDiagonal();
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265
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266 Returns 1 or 0 based on whether *Matrix* is a lower bidiagonal
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267 matrix.
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268
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269 A matrix is a lower bidiagonal matrix:
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270
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271 . It's a square matrix
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272 . All its main diagonal and lower diagonal elements are non-zeros and all its
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273 other elements are zeros
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274
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275 IsLowerTriangular
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276 $Status = $Matrix->IsLowerTriangular();
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277
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278 Returns 1 or 0 based on whether *Matrix* is a left or lower
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279 triangular matrix.
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280
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281 A matrix is a lower triangular matrix:
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282
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283 . It's a square matrix
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284 . All its entries above the main diagonal are zero
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285
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286 IsLowerUniTriangular
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287 $Status = $Matrix->IsLowerUniTriangular();
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288
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289 Returns 1 or 0 based on whether *Matrix* is a lower triangular
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290 matrix.
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291
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292 IsMatrix
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293 $Status = Matrix::IsMatrix($Object);
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294
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295 Returns 1 or 0 based on whether *Object* is a Matrix object.
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296
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297 IsNegative
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298 $Status = $Matrix->IsNegative();
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299
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300 Returns 1 or 0 based on whether *Matrix* is a negative matrix
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301 containing only values less than or equal to zero.
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302
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303 IsPositive
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304 $Status = $Matrix->IsPositive();
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305
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306 Returns 1 or 0 based on whether *Matrix* is a negative matrix
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307 containing only values greater than or equal to zero.
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308
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309 IsRightTriangular
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310 $Status = $Matrix->IsRightTriangular();
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311
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312 Returns 1 or 0 based on whether *Matrix* is a right or upper
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313 triangular matrix.
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314
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315 IsSkewSymmetric
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316 $Status = $Matrix->IsSkewSymmetric();
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317
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318 Returns 1 or 0 based on whether *Matrix* is a skew or anti symmetric
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319 matrix.
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320
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321 IsSquare
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322 $Status = $Matrix->IsSquare();
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323
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324 Returns 1 or 0 based on whether *Matrix* is a square matrix
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325 containing equal number of rows and columns.
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326
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327 IsStrictlyLowerTriangular
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328 $Status = $Matrix->IsStrictlyLowerTriangular();
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329
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330 Returns 1 or 0 based on whether *Matrix* is a strictly lower
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331 triangular matrix.
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332
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333 A matrix is a strictly lower triangular matrix:
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334
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335 . It's a square matrix
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336 . All its entries on and above the main diagonal are zero
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337
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338 IsStrictlyUpperTriangular
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339 $Status = $Matrix->IsStrictlyUpperTriangular();
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340
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341 Returns 1 or 0 based on whether *Matrix* is a strictly upper
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342 triangular matrix.
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343
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344 A matrix is a strictly upper triangular matrix:
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345
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346 . It's a square matrix
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347 . All its entries on and below the main diagonal are zero
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348
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349 IsSymmetric
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350 $Status = $Matrix->IsSymmetric();
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351
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352 Returns 1 or 0 based on whether *Matrix* is a symmetric matrix.
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353
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354 A matrix is a symmetric matrix:
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355
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356 . It's a square matrix
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357 . Its elements are symmetric with respect to main diagonal. In other words,
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358 elements below the main diagonal are equal to the elements above the main
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359 diagonal.
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360
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361 Transpose of a symmetric matrix equals the matrix itself.
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362
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363 IsTriDiagonal
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364 $Status = $Matrix->IsTriDiagonal();
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365
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366 Returns 1 or 0 based on whether *Matrix* is a tridiagonal matrix.
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367
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368 A matrix is a tribidiagonal matrix:
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369
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370 . It's a square matrix
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371 . All its main diagonal, upper diagonal, and lower diagonal elements are non-zeros and all its
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372 other elements are zeros
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373
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374 IsUnit
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375 $Status = $Matrix->IsUnit();
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376
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377 Returns 1 or 0 based on whether *Matrix* is a unit matrix.
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378
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379 A matrix is a unit matrix:
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380
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381 . It's a square matrix
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382 . All its diagonal elements are ones and its off-diagonal elements are zeros
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383
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384 IsUnitLowerTriangular
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385 $Status = $Matrix->IsUnitLowerTriangular();
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386
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387 Returns 1 or 0 based on whether *Matrix* is an unit lower triangular
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388 matrix.
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389
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390 A matrix is an unit lower triangular matrix:
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391
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392 . It's a square matrix
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393 . All its entries main diagonal are one
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394 . All its entries above the main diagonal are zero
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395
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396 IsUnitUpperTriangular
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397 $Status = $Matrix->IsUnitUpperTriangular();
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398
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399 Returns 1 or 0 based on whether *Matrix* is an unit upper triangular
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400 matrix.
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401
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402 A matrix is an unit upper triangular matrix:
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403
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404 . It's a square matrix
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405 . All its entries main diagonal are one
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406 . All its entries below the main diagonal are zero
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407
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408 IsUpperBiDiagonal
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409 $Status = $Matrix->IsUpperBiDiagonal();
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410
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411 Returns 1 or 0 based on whether *Matrix* is an upper bidiagonal
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412 matrix.
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413
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414 A matrix is an upper bidiagonal matrix:
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415
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416 . It's a square matrix
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417 . All its main diagonal and upper diagonal elements are non-zeros and all its
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418 other elements are zeros
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419
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420 IsUpperTriangular
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421 $Status = $Matrix->IsUpperTriangular();
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422
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423 Returns 1 or 0 based on whether *Matrix* is a right or upper
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424 triangular matrix.
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425
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426 A matrix is an upper triangular matrix:
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427
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428 . It's a square matrix
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429 . All its entries below the main diagonal are zero
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430
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431 IsUpperUniTriangular
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432 $Status = $Matrix->IsUpperUniTriangular();
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433
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434 Returns 1 or 0 based on whether *Matrix* is a right or upper
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435 triangular matrix.
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436
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437 NewFromColumns
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438 $NewMatrix = Matrix::NewFromColumns($Col1Vector, $Col2Vector, ...);
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439 $NewMatrix = Matrix::NewFromColumns($Col1ValuesRef, $Col2ValuesRef, ...);
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440 $NewMatrix = Matrix::NewFromColumns("Val1 Val2 ...", "Val1 Val2", ...);
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441
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442 $NewMatrix = $Matrix->NewFromColumns($Col1Vector, $Col2Vector, ...);
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443 $NewMatrix = $Matrix->NewFromColumns($Col1ValuesRef, $Col2ValuesRef, ...);
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444 $NewMatrix = $Matrix->NewFromColumns("Val1 Val2 ...", "Val1 Val2", ...);
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445
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446 Creates a new Matrix using specified column values and returns
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447 NewMatrix object.
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448
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449 The column values can be specified in one of the following formats:
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450
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451 . List of vector objects
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452 . References to list of values
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453 . List of strings containing columns values delimited by space
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454
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455 Each column must contain the same number of values.
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456
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457 NewFromDiagonal
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458 $NewMatrix = Matrix::NewFromDiagonal($DiagonalVector);
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459 $NewMatrix = Matrix::NewFromDiagonal($DiagonalValuesRef);
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460 $NewMatrix = Matrix::NewFromDiagonal("Val1 Val2 ...");
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461
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462 $NewMatrix = Matrix->NewFromDiagonal($DiagonalVector);
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463 $NewMatrix = Matrix->NewFromDiagonal($DiagonalValuesRef);
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464 $NewMatrix = Matrix->NewFromDiagonal("Val1 Val2 ...");
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465
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466 Creates a new Matrix using specified diagonal values and returns
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467 NewMatrix object.
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468
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469 The column values can be specified in one of the following formats:
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470
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471 . A vector object
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472 . Reference to list of values
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473 . Strings containing diagonal values delimited by space
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474
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475 NewFromRows
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476 $NewMatrix = Matrix::NewFromRows($Row1Vector, $RowVector, ...);
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477 $NewMatrix = Matrix::NewFromRows($Row1ValuesRef, $Row2ValuesRef, ...);
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478 $NewMatrix = Matrix::NewFromRows("Val1 Val2 ...", "Val1 Val2", ...);
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479
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480 $NewMatrix = $Matrix->NewFromRows($Row1Vector, $Row2Vector, ...);
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481 $NewMatrix = $Matrix->NewFromRows($Row1ValuesRef, $Row2ValuesRef, ...);
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482 $NewMatrix = $Matrix->NewFromRows("Val1 Val2 ...", "Val1 Val2", ...);
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483
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484 Creates a new Matrix using specified row values and returns
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485 NewMatrix object.
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486
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487 The row values can be specified in one of the following formats:
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488
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489 . List of vector objects
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490 . References to list of values
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491 . List of strings containing columns values delimited by space
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492
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493 Each row must contain the same number of values.
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494
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495 One
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496 $Matrix->One();
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497
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498 Sets values of all *Matrix* elements to 1 and returns *Matrix*.
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499
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500 SetAllValues
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501 $Matrix->SetAllValues($Value);
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502
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503 Sets values of all *Matrix* elements to specified *Value* and
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504 returns *Matrix*.
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505
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506 SetColumnValues
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507 $Matrix->SetColumnValues($ColIndex, @Values);
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508 $Matrix->SetColumnValues($ColIndex, \@Values);
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509 $Matrix->SetColumnValues($ColIndex, $VectorObject);
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510 $Matrix->SetColumnValues($ColIndex, "Value1 Value2 Value3 ...");
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511
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512 Sets column values of a specified *ColIndex* of *Matrix* using an
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513 array, reference to an array, another vector, or space delimited
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514 value string and returns *Matrix*.
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515
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516 SetDiagonalValues
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517 $Matrix->SetDiagonalValues(@Values);
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518 $Matrix->SetDiagonalValues(\@Values);
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519 $Matrix->SetDiagonalValues($VectorObject);
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520 $Matrix->SetDiagonalValues("Value1 Value2 Value3 ...");
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521
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522 Sets values of the diagonal in square *Matrix* and returns *Matrix*.
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523
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524 SetMatrixPrintStyle
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525 $Matrix->SetMatrixPrintStyle($MatrixStyle);
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526 $Matrix::SetMatrixPrintStyle($MatrixStyle);
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527
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528 Sets print style for matrix rows for an individual object or the
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529 whole class during StringifyMatrix operation. Possible *MatrixStyle*
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530 values: *AllRowsInOneLine, OneRowPerLine*. Default:
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531 *AllRowsInOneLine*.
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532
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533 SetRowValues
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534 $Matrix->SetRowValues($ColIndex, @Values);
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535 $Matrix->SetRowValues($ColIndex, \@Values);
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536 $Matrix->SetRowValues($ColIndex, $VectorObjext);
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537 $Matrix->SetRowValues($ColIndex, "Value1 Value2 Value3 ...");
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538
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539 Sets row values of a specified *RowIndex* of *Matrix* using an
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540 array, reference to an array, another vector, or space delimited
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541 value string and returns *Matrix*.
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542
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543 SetValue
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544 $Matrix->SetValue($RowIndex, $ColIndex, $Value, [$SkipIndexCheck]);
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545
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546 Sets Value of *Matrix* element specified using *RowIndex* and
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547 *ColIndex* with indicies starting at 0 with optional validation of
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548 specified index values and return *Matrix*.
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549
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550 SetValuePrintFormat
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551 $Matrix->SetValuePrintFormat($ValueFormat);
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552 $Matrix::SetValuePrintFormat($ValueFormat);
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553
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554 Sets value print format for an individual object or the whole class
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555 during StringifyMatrix operation and returns *Matrix*.
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556
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557 StringifyMatrix
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558 $String = $Matrix->StringifyMatrix();
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559
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560 Returns a string containing information about *Matrix* object.
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561
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562 Transpose
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563 $Matrix->Transpose();
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564
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565 Transposes *Matrix* by swaping rows with columns and returns
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566 *Matrix*.
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567
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568 UnitMatrix
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569 $NewUnitMatrix = $Matrix::UnitMatrix($NumOfRows, $NumOfCols);
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570 $NewUnitMatrix = $Matrix::UnitMatrix();
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571 $NewUnitMatrix = $Matrix->UnitMatrix($NumOfRows, $NumOfCols);
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572
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573 Creates a new UnitMatrix of specified size *NumOfRows x NumOfCol* or
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574 of size 3 x 3 and returns NewUnitMatrix object.
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575
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576 Zero
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577 $Matrix->Zero();
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578
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579 Sets values of all *Matrix* elements to 0 and returns *Matrix*.
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580
|
|
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581 ZeroMatrix
|
|
|
582 $NewZeroMatrix = $Matrix::ZeroMatrix($NumOfRows, $NumOfCols);
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|
583 $NewZeroMatrix = $Matrix::ZeroMatrix();
|
|
|
584 $NewZeroMatrix = $Matrix->ZeroMatrix($NumOfRows, $NumOfCols);
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585
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586 Creates a new ZeroMatrix of specified size *NumOfRows x NumOfCol* or
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587 of size 3 x 3 and returns NewZeroMatrix object.
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588
|
|
|
589 AUTHOR
|
|
|
590 Manish Sud <msud@san.rr.com>
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|
|
591
|
|
|
592 SEE ALSO
|
|
|
593 Vector.pm
|
|
|
594
|
|
|
595 COPYRIGHT
|
|
|
596 Copyright (C) 2015 Manish Sud. All rights reserved.
|
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|
597
|
|
|
598 This file is part of MayaChemTools.
|
|
|
599
|
|
|
600 MayaChemTools is free software; you can redistribute it and/or modify it
|
|
|
601 under the terms of the GNU Lesser General Public License as published by
|
|
|
602 the Free Software Foundation; either version 3 of the License, or (at
|
|
|
603 your option) any later version.
|
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604
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