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1.矩阵的加法
数学定义:设有两个m*n的矩阵A和B,那么矩阵A与B的和记作A+B,规定其内的元素为A,B内对应元素的和.
*矩阵加法满足交换律和结合律
*矩阵减法：A-B=A+(-B)
‘重载矩阵加法 Public Overloads Shared Operator +(ByVal leftMatrix As Matrix, ByVal RightMatrix As Matrix) As Matrix Dim leftRow, leftCol, rightRow, rightCol As Integer leftRow = leftMatrix.Row : leftCol = leftMatrix.Col ‘被加矩阵的行与列长度 rightRow = RightMatrix.Row : rightCol = RightMatrix.Col ‘相加矩阵的行与列长度 If leftRow = rightRow And leftCol = rightCol Then Dim tempMatrix As New Matrix(leftRow, leftCol) For i = 1 To leftRow For j = 1 To leftCol tempMatrix.Item(i, j) = leftMatrix.Item(i, j) + RightMatrix.Item(i, j) ‘对应元素相加 Next Next Return tempMatrix Else Return Nothing End If End Operator ‘重载矩阵减法 Public Overloads Shared Operator -(ByVal leftMatrix As Matrix, ByVal RightMatrix As Matrix) As Matrix Dim leftRow, leftCol, rightRow, rightCol As Integer leftRow = leftMatrix.Row : leftCol = leftMatrix.Col ‘被减矩阵的行与列长度 rightRow = RightMatrix.Row : rightCol = RightMatrix.Col ‘相减矩阵的行与列长度 If leftRow = rightRow And leftCol = rightCol Then Dim tempMatrix As New Matrix(leftRow, leftCol) For i = 1 To leftRow For j = 1 To leftCol tempMatrix.Item(i, j) = leftMatrix.Item(i, j) - RightMatrix.Item(i, j) ‘对应元素相减 Next Next Return tempMatrix Else Return Nothing End If End Operator
2.数与矩阵相乘
数学定义:设数λ和矩阵A,那么λ与矩阵A的乘积记作λA,规定其内的元素为A,B内对应元素的乘积.
*数与矩阵相乘满足交换律,结合律和分配律
*矩阵加法与数乘矩阵统称为矩阵的线性运算
‘重载数与矩阵相乘 Public Overloads Shared Operator *(ByVal leftNum As Integer, ByVal RightMatrix As Matrix) As Matrix Dim rightRow, rightCol As Integer rightRow = RightMatrix.Row : rightCol = RightMatrix.Col ‘相加矩阵的行与列长度 Dim tempMatrix As New Matrix(rightRow, rightCol) For i = 1 To rightRow For j = 1 To rightCol tempMatrix.Item(i, j) = RightMatrix.Item(i, j) * leftNum ‘对应元素相加 Next Next Return tempMatrix End Operator ‘重载矩阵与数相乘（交换律） Public Overloads Shared Operator *(ByVal RightMatrix As Matrix, ByVal leftNum As Integer) As Matrix Dim rightRow, rightCol As Integer rightRow = RightMatrix.Row : rightCol = RightMatrix.Col ‘相加矩阵的行与列长度 Dim tempMatrix As New Matrix(rightRow, rightCol) For i = 1 To rightRow For j = 1 To rightCol tempMatrix.Item(i, j) = RightMatrix.Item(i, j) * leftNum ‘对应元素相加 Next Next Return tempMatrix End Operator
3.矩阵与矩阵相乘
数学定义:设A是一个m*s的矩阵,B是一个s*n的矩阵，那么规定矩阵A与矩阵B的乘积是一个s*n的矩阵C,规定其i行j列的元素为A的i行与B的j列内对应元素的乘积和.
*矩阵与矩阵相乘满足结合律和分配律,但不满足交换律
‘重载矩阵乘法 Public Overloads Shared Operator *(ByVal leftMatrix As Matrix, ByVal RightMatrix As Matrix) As Matrix Dim leftRow, leftCol, rightRow, rightCol As Integer leftRow = leftMatrix.Row : leftCol = leftMatrix.Col ‘被乘矩阵的行与列长度 rightRow = RightMatrix.Row : rightCol = RightMatrix.Col ‘相乘矩阵的行与列长度 If leftCol = rightRow Then Dim tempMatrix As New Matrix(leftRow, rightCol) For i = 1 To leftRow For j = 1 To rightCol For k = 1 To leftCol tempMatrix.Item(i, j) = tempMatrix.Item(i, j) + leftMatrix.Item(i, k) * RightMatrix.Item(k, j) ‘对应元素相加 Next Next Next Return tempMatrix Else Return Nothing End If End Operator
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原文地址：http://www.cnblogs.com/experdot/p/4392817.html
