C#矩阵类运算

/// <summary>
  /// 矩阵类
 /// </summary>
 /// </remarks>
 public sealed class Matrix
 {
     int row, column;            //矩阵的行列数
     double [,] data;            //矩阵的数据
 
     #region 构造函数
     public Matrix(int rowNum,int columnNum)
     {
         row = rowNum;
         column = columnNum;
         data = new double[row, column];
     }
     public Matrix(double[,] members)
     {
         row = members.GetUpperBound(0) + 1;
         column = members.GetUpperBound(1) + 1;
         data = new double[row, column];
         Array.Copy(members, data, row * column);
     }
     public Matrix(double[] vector)
     {
         row = 1;
         column = vector.GetUpperBound(0)+1;
         data = new double[1, column];
         for (int i = 0; i < vector.Length; i++)
         {
             data[0, i] = vector[i];
         }
     }
     #endregion
 
 
     #region 属性和索引器
     public int rowNum { get { return row; } }
     public int columnNum { get { return column; } }
 
     public double this [int r,int c]
     {
         get{ return data[r,c];}
         set{data[r,c]=value;}
     }
     #endregion
 
 
 
     #region 转置
     /// <summary>
     /// 将矩阵转置，得到一个新矩阵（此操作不影响原矩阵）
     /// </summary>
     /// <param name="input">要转置的矩阵</param>
     /// <returns>原矩阵经过转置得到的新矩阵</returns>
     public static Matrix transpose(Matrix input)
     {
         double[,] inverseMatrix = new double[input.column, input.row];
         for (int r = 0; r < input.row; r++)          
             for (int c = 0; c < input.column; c++)               
                 inverseMatrix[c, r] = input[r, c];
         return new Matrix(inverseMatrix);
     }
     #endregion
 
     #region 得到行向量或者列向量
     public Matrix getRow(int r)
     {
         if (r > row || r<=0) throw new MatrixException("没有这一行。");
         double[] a = new double[column];
         Array.Copy(data,  column * (row - 1), a, 0, column);
         Matrix m = new Matrix(a);           
         return m;
     }
     public Matrix getColumn(int c)
     {
         if (c > column || c < 0) throw new MatrixException("没有这一列。");
         double[,] a = new double[row,1];
         for (int i = 0; i < row; i++)           
             a[i,0] = data[i, c];
         return new Matrix(a);
     }
     #endregion
 
     #region 操作符重载  + - * / == !=
     public static Matrix operator +(Matrix a, Matrix b)
     {
         if (a.row != b.row || a.column != b.column)
             throw new MatrixException("矩阵维数不匹配。");
         Matrix result = new Matrix(a.row, a.column);
         for (int i = 0; i < a.row; i++)          
             for (int j = 0; j < a.column; j++)               
                 result[i, j] = a[i, j] + b[i, j];
         return result;
     }
 
     public static Matrix operator -(Matrix a, Matrix b)
     {
         return a + b * (-1);
     }
 
     public static Matrix operator *(Matrix matrix, double factor)
     {
         Matrix result = new Matrix(matrix.row, matrix.column);
         for (int i = 0; i < matrix.row; i++)           
             for (int j = 0; j < matrix.column; j++)              
                 matrix[i, j] = matrix[i, j] * factor;
         return matrix;
     }
     public static Matrix operator *(double factor,Matrix matrix)
     {
         return matrix * factor;
     }
     public static Matrix operator *(Matrix a, Matrix b)
     {
         if(a.column!=b.row)
             throw new MatrixException("矩阵维数不匹配。");
         Matrix result = new Matrix(a.row, b.column);
         for (int i = 0; i < a.row; i++)           
             for (int j = 0; j < b.column; j++)               
                 for (int k = 0; k < a.column; k++)                   
                     result[i, j] += a[i, k] * b[k, j];
                
         return result;
     }
     public static bool operator ==(Matrix a, Matrix b)
     {
         if (object.Equals(a, b)) return true;
         if(object.Equals(null,b))
             return a.Equals(b);
         return b.Equals(a);
     }
     public static bool operator !=(Matrix a, Matrix b)
     {
         return !(a == b);
     }
     public override bool Equals(object obj)
     {
         if (obj == null) return false;
         if (!(obj is Matrix)) return false;
         Matrix t = obj as Matrix;
         if (row != t.row || column != t.column) return false;
         return this.Equals(t, 10);
     }
     /// <summary>
     /// 按照给定的精度比较两个矩阵是否相等
     /// </summary>
     /// <param name="matrix">要比较的另外一个矩阵</param>
     /// <param name="precision">比较精度（小数位）</param>
     /// <returns>是否相等</returns>
     public bool Equals(Matrix matrix, int precision)
     {
         if (precision < 0)  throw new MatrixException("小数位不能是负数");
         double test = Math.Pow(10.0, -precision);
         if (test<double.Epsilon)           
             throw new MatrixException("所要求的精度太高，不被支持。");
         for (int r = 0; r < this.row; r++)           
             for (int c = 0; c < this.column; c++)               
                 if (Math.Abs(this[r, c] - matrix[r, c] )>=test)
                     return false;
 
         return true;
     }
     #endregion
 }