本类我是用VB.NET编写的类，不管用什么语言，算法都类似，注释写得都挺详尽的了，而且我也通过了调试。

Public Class Matrix

Private matrix(,) As Double '定义矩阵变量 Private rowbound As Integer '定义数组行数，从0开始 Private colbound As Integer '定义数组列数，从0开始 Public Sub New(ByVal data(,) As Double) '首先获得矩阵大小 rowbound = data.GetUpperBound(0) colbound = data.GetUpperBound(1) ReDim matrix(rowbound,colbound) Dim i As Integer,j As Integer '数组赋值循环变量 For i = 0 To rowbound '赋值到矩阵变量 For j = 0 To colbound matrix(i,j) = data(i,j) Next j Next i End Sub '构造函数 Public Sub LetMatrix(ByRef output_(,) As Double) Dim i As Integer,j As Integer For i = 0 To rowbound For j = 0 To colbound output_(i,j) = matrix(i,j) Next j Next i End Sub '把类中的矩阵输出到一个二维数组中 Public Sub SetMatrix(ByVal input_(,) As Double) ReDim matrix(input_.GetUpperBound(0),input_.GetUpperBound(1)) Dim i As Integer,j As Integer '数组赋值循环变量 For i = 0 To input_.GetUpperBound(0) '赋值到矩阵变量 For j = 0 To input_.GetUpperBound(1) matrix(i,j) = input_(i,j) Next j Next i End Sub '把一个二维数组中数据输出到类中 Public Function GetTranspose() As Matrix Dim output_(,) As Double ReDim output_(rowbound,colbound) LetMatrix(output_) Dim i As Integer,j As Integer,t As Double For i = 0 To rowbound For j = i To colbound t = output_(i,j) output_(i,j) = output_(j,i) output_(j,i) = t Next Next Return New Matrix(output_) End Function '得到原矩阵的转置 Public Function GetValue() As Double '求行列式的值,矩阵必须是方阵 Dim value As Double '用于保存行列式的值 value = 1 '求值基本思路：通过高斯消去法进行矩阵变换，形成三角行列式 Dim Ri As Integer,Rj As Integer '用于行列之间循环,Ri为行 Dim t As Integer '临时变量t用于循环 Ri = 0 Rj = 0 Dim minus As Integer '记录矩阵变换后的正负号 minus = 1 Dim k As Double '为了将行列式某些值变成0，必须配个比例系数k，使得 R(a)-k*R(b)=0 Dim matrix_(,) As Double '定义临时矩阵 ReDim matrix_(rowbound,colbound) For Ri = 0 To rowbound '为了防止原始矩阵被修改，赋值到临时矩阵 For Rj = 0 To colbound matrix_(Ri,Rj) = matrix(Ri,Rj) Next Rj Next Ri For Rj = 0 To rowbound '从最左行开始化上三角 For Ri = rowbound To Rj + 1 Step -1 '从最下边开始化上三角 If matrix_(Ri - 1,Rj) = 0 Then SwapRow(matrix_,Ri - 1,Ri) '如果上一行的对应数字为0，则交换这两行行列式 minus = minus * -1 End If If matrix_(Ri - 1,Rj) <> 0 Then k = -1 * matrix_(Ri,Rj) / matrix_(Ri - 1,Rj) '比例系数则等于下行数字除以上行 For t = Rj To rowbound matrix_(Ri,t) = matrix_(Ri,t) + k * matrix_(Ri - 1,t) '高斯变换原理 Next t Next Ri Next Rj For t = 0 To rowbound '计算上三角行列式的值 value = value * matrix_(t,t) Next value = value * minus 'If value=#IND then value=0 Return value End Function '输出行列式的值 Public Function GetInverse() As Matrix '求逆矩阵 '定义类和数据，进行返回 Dim result As Matrix Dim data(,) As Double ReDim data(rowbound,colbound) Dim matrix_(,) As Double '定义临时矩阵 Dim tmatrix As Matrix '定义临时矩阵类 Dim i As Integer,j As Integer '临时变量用于循环 ReDim matrix_(rowbound,colbound) For i = 0 To rowbound '为了防止原始矩阵被修改，赋值到临时矩阵 For j = 0 To colbound matrix_(i,j) Next j Next i If GetValue() = 0 Then Debug.Print("该矩阵没有逆矩阵，因为行列式的值为0") Return Nothing ElseIf rowbound <> colbound Then Debug.Print("该矩阵没有逆矩阵，因为不是方阵") Return Nothing End If '接下来获得伴随矩阵和逆矩阵 For i = 0 To rowbound For j = 0 To colbound tmatrix = New Matrix(matrix) '实例化临时矩阵 tmatrix = tmatrix.DelRow(tmatrix.matrix,i) tmatrix = tmatrix.DelCol(tmatrix.matrix,j) '先删除某一行，再删除某一列，得到伴随矩阵子块 matrix_(j,i) = ((tmatrix.GetValue) * (-1) ^ (i + j + 2)) / GetValue() '去掉某行某列以得到伴随矩阵子块，并求出其值，除以原矩阵的行列式则得到逆矩阵 Next j Next i result = New Matrix(matrix_) Return result End Function '输出逆矩阵 Public Shared Operator *(ByVal m1 As Matrix,ByVal m2 As Matrix) As Matrix Dim md1(,) As Double,md2(,) As Double '存储m1,m2矩阵数据 Dim result(,) As Double '存储运算结果 Dim t As Double '存储每一个值的临时结果 Dim i As Integer,k As Integer '注意：仅仅当坐矩阵列数等于右矩阵行数时才可以进行乘法 If m1.colbound <> m2.rowbound Then Debug.Print("无法进行矩阵乘法运算，矩阵一的列数不等于矩阵二的行数。") Return Nothing End If ReDim md1(m1.rowbound,m1.colbound) ReDim md2(m2.rowbound,m2.colbound) ReDim result(m1.rowbound,m2.colbound) m1.LetMatrix(md1) m2.LetMatrix(md2) For i = 0 To m2.colbound For j = 0 To m1.rowbound t = 0 For k = 0 To m1.colbound t = t + md1(j,k) * md2(k,i) Next result(j,i) = t Next j Next i Return New Matrix(result) End Operator '重载*运算符，定义矩阵间的乘法运算，计算m1 * m2 Public Shared Operator +(ByVal m1 As Matrix,) As Double '存储运算结果 Dim i As Integer,j As Integer '注意：只有两个矩阵的长宽一样才可以进行运算 If m1.rowbound <> m2.rowbound Or m1.colbound <> m2.colbound Then Debug.Print("无法进行矩阵加法运算，长宽不一致。") Return Nothing End If ReDim result(m1.rowbound,m1.colbound) ReDim md1(m1.rowbound,m2.colbound) m1.LetMatrix(md1) m2.LetMatrix(md2) For i = 0 To m1.rowbound For j = 0 To m1.colbound result(i,j) = md1(i,j) + md2(i,j) Next j Next i Return New Matrix(result) End Operator '重载+运算符，定义矩阵间的加法运算，计算m1 + m2 Public Shared Operator -(ByVal m1 As Matrix,j As Integer '注意：只有两个矩阵的长宽一样才可以进行运算 If m1.rowbound <> m2.rowbound Or m1.colbound <> m2.colbound Then Debug.Print("无法进行矩阵减法运算，长宽不一致。") Return Nothing End If ReDim result(m1.rowbound,j) - md2(i,j) Next j Next i Return New Matrix(result) End Operator '重载-运算符，定义矩阵间的减法运算，计算m1 - m2 Private Function DelRow(ByVal matrix_(,ByVal r As Integer) As Matrix '删除某行 Dim i As Integer,j As Integer For i = r To matrix_.GetUpperBound(0) - 1 For j = 0 To matrix_.GetUpperBound(1) matrix_(i,j) = matrix_(i + 1,j) '把下面的值赋给上面的值 Next j Next i Dim result(,) As Double ReDim result(matrix_.GetUpperBound(0) - 1,matrix_.GetUpperBound(1)) '重新修改边界 For i = 0 To matrix_.GetUpperBound(0) - 1 For j = 0 To matrix_.GetUpperBound(1) result(i,j) Next j Next i Return New Matrix(result) End Function '删除某一行 Private Function DelCol(ByVal matrix_(,ByVal c As Integer) As Matrix '删除某列 Dim i As Integer,j As Integer For i = 0 To matrix_.GetUpperBound(0) For j = c To matrix_.GetUpperBound(1) - 1 matrix_(i,j) = matrix_(i,j + 1) '把右边的值赋给左边的值 Next j Next i Dim result(,) As Double ReDim result(matrix_.GetUpperBound(0),matrix_.GetUpperBound(1) - 1) '重新修改边界 For i = 0 To matrix_.GetUpperBound(0) For j = 0 To matrix_.GetUpperBound(1) - 1 result(i,j) Next j Next i Return New Matrix(result) End Function '删除某一列 Private Sub SwapRow(ByRef matrix_(,ByVal i As Integer,ByVal j As Integer) '交换矩阵两列 Dim t As Integer '临时变量t，用于循环 Dim temp As Double 'temp变量用于交换 For t = 0 To rowbound temp = matrix_(i,t) matrix_(i,t) = matrix_(j,t) matrix_(j,t) = temp Next End Sub '交换某两行 End Class '矩阵类，进行简单矩阵计算