/// <summary>
/// 把矩陣分解為對稱矩陣與反稱矩陣之和：對稱矩陣
/// </summary>
/// <param name="matrix">矩陣</param>
/// <returns></returns>
private static double[][] SymmetricPart(double[][] matrix)
{
 //合法性校驗：矩陣必須為方陣
 if ( MatrixCR(matrix)[0] != MatrixCR(matrix)[1])
 {
  throw new Exception("matrix 不是一個方陣");
 }
 //矩陣中沒有元素的情況
 if (matrix.Length == 0)
 {
  return new double[][] { };
 }
 //生成一個與matrix同型的空矩陣
 double[][] result = new double[matrix.Length][];
 for (int i = 0; i < result.Length; i++)
 {
  result[i] = new double[matrix[i].Length];
 }
 //對稱矩陣為 (A+T(A))/2 其中A為原矩陣，T(A)為A的轉置矩陣
 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;
}

3.求出反稱矩陣部分的函數(shù)

/// <summary>
/// 把矩陣分解為對稱矩陣與反稱矩陣之和：反稱矩陣
/// </summary>
/// <param name="matrix">矩陣</param>
/// <returns></returns>
private static double[][] SkewSymmetricPart(double[][] matrix)
{
 //合法性校驗：矩陣必須為方陣
 if (MatrixCR(matrix)[0] != MatrixCR(matrix)[1])
 {
  throw new Exception("matrix 不是一個方陣");
 }
 //矩陣中沒有元素的情況
 if (matrix.Length == 0)
 {
  return new double[][] { };
 }
 //生成一個與matrix同型的空矩陣
 double[][] result = new double[matrix.Length][];
 for (int i = 0; i < result.Length; i++)
 {
  result[i] = new double[matrix[i].Length];
 }
 //反稱矩陣為 (A-T(A))/2 其中A為原矩陣，T(A)為A的轉置矩陣
 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;
}

4.其他函數(shù)

/// <summary>
/// 判斷一個二維數(shù)組是否為矩陣
/// </summary>
/// <param name="matrix">二維數(shù)組</param>
/// <returns>true:是矩陣 false:不是矩陣</returns>
private static bool isMatrix(double[][] matrix)
{
 //空矩陣是矩陣
 if (matrix.Length < 1) return true;
 //不同行列數(shù)如果不相等，則不是矩陣
 int count = matrix[0].Length;
 for (int i = 1; i < matrix.Length; i++)
 {
  if (matrix[i].Length != count)
  {
   return false;
  }
 }
 //各行列數(shù)相等，則是矩陣
 return true;
}
/// <summary>
/// 計算一個矩陣的行數(shù)和列數(shù)
/// </summary>
/// <param name="matrix">矩陣</param>
/// <returns>數(shù)組：行數(shù)、列數(shù)</returns>
private static int[] MatrixCR(double[][] matrix)
{
 //接收到的參數(shù)不是矩陣則報異常
 if (!isMatrix(matrix))
 {
  throw new Exception("接收到的參數(shù)不是矩陣");
 }
 //空矩陣行數(shù)列數(shù)都為0
 if (!isMatrix(matrix) || matrix.Length == 0)
 {
  return new int[2] { 0, 0 };
 }
 return new int[2] { matrix.Length, matrix[0].Length };
}
/// <summary>
/// 打印矩陣
/// </summary>
/// <param name="matrix">待打印矩陣</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");
   //注意不能寫為：Console.Write(matrix[i][j] + '\t');
  }
  Console.WriteLine();
 }
}

5.Main函數(shù)代碼及程序運行示例

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("原矩陣");
 PrintMatrix(matrix);
 Console.WriteLine("對稱矩陣");
 PrintMatrix(SymmetricPart(matrix));
 Console.WriteLine("反稱矩陣");
 PrintMatrix(SkewSymmetricPart(matrix));
 Console.ReadLine();
}

運行效果如下圖所示：