C#实现将一个矩阵分解为对称矩阵与反称矩阵之和的方法

/// <summary>/// 把矩阵分解为对称矩阵与反称矩阵之和：对称矩阵/// </summary>/// <param name="matrix">矩阵</param>/// <returns></returns>private static double[][] SymmetricPart(double[][] matrix){ //合法性校验：矩阵必须为方阵 if ( MatrixCR(matrix)[0] != MatrixCR(matrix)[1]) {  throw new Exception("matrix 不是一个方阵"); } //矩阵中没有元素的情况 if (matrix.Length == 0) {  return new double[][] { }; } //生成一个与matrix同型的空矩阵 double[][] result = new double[matrix.Length][]; for (int i = 0; i < result.Length; i++) {  result[i] = new double[matrix[i].Length]; } //对称矩阵为 (A+T(A))/2 其中A为原矩阵，T(A)为A的转置矩阵 for (int i = 0; i < result.Length; i++) {  for (int j = 0; j < result.Length; j++)  {   result[i][j] = (matrix[i][j] + matrix[j][i]) / 2.0;  } } return result;}

/// <summary>/// 把矩阵分解为对称矩阵与反称矩阵之和：反称矩阵/// </summary>/// <param name="matrix">矩阵</param>/// <returns></returns>private static double[][] SkewSymmetricPart(double[][] matrix){ //合法性校验：矩阵必须为方阵 if (MatrixCR(matrix)[0] != MatrixCR(matrix)[1]) {  throw new Exception("matrix 不是一个方阵"); } //矩阵中没有元素的情况 if (matrix.Length == 0) {  return new double[][] { }; } //生成一个与matrix同型的空矩阵 double[][] result = new double[matrix.Length][]; for (int i = 0; i < result.Length; i++) {  result[i] = new double[matrix[i].Length]; } //反称矩阵为 (A-T(A))/2 其中A为原矩阵，T(A)为A的转置矩阵 for (int i = 0; i < result.Length; i++) {  for (int j = 0; j < result.Length; j++)  {   result[i][j] = (matrix[i][j] - matrix[j][i]) / 2.0;  } } return result;}

/// <summary>/// 判断一个二维数组是否为矩阵/// </summary>/// <param name="matrix">二维数组</param>/// <returns>true:是矩阵 false:不是矩阵</returns>private static bool isMatrix(double[][] matrix){ //空矩阵是矩阵 if (matrix.Length < 1) return true; //不同行列数如果不相等，则不是矩阵 int count = matrix[0].Length; for (int i = 1; i < matrix.Length; i++) {  if (matrix[i].Length != count)  {   return false;  } } //各行列数相等，则是矩阵 return true;}/// <summary>/// 计算一个矩阵的行数和列数/// </summary>/// <param name="matrix">矩阵</param>/// <returns>数组：行数、列数</returns>private static int[] MatrixCR(double[][] matrix){ //接收到的参数不是矩阵则报异常 if (!isMatrix(matrix)) {  throw new Exception("接收到的参数不是矩阵"); } //空矩阵行数列数都为0 if (!isMatrix(matrix) || matrix.Length == 0) {  return new int[2] { 0, 0 }; } return new int[2] { matrix.Length, matrix[0].Length };}/// <summary>/// 打印矩阵/// </summary>/// <param name="matrix">待打印矩阵</param>private static void PrintMatrix(double[][] matrix){ for (int i = 0; i < matrix.Length; i++) {  for (int j = 0; j < matrix[i].Length; j++)  {   Console.Write(matrix[i][j] + "/t");   //注意不能写为：Console.Write(matrix[i][j] + '/t');  }  Console.WriteLine(); }}

static void Main(string[] args){ double[][] matrix = new double[][]  {  new double[] { 1, 2, 3 },  new double[] { 4, 5, 6 },  new double[] { 7, 8, 9 } }; Console.WriteLine("原矩阵"); PrintMatrix(matrix); Console.WriteLine("对称矩阵"); PrintMatrix(SymmetricPart(matrix)); Console.WriteLine("反称矩阵"); PrintMatrix(SkewSymmetricPart(matrix)); Console.ReadLine();}