/// <summary>
/// 檢查一個(gè)矩陣是否為對(duì)稱(chēng)矩陣
/// </summary>
/// <param name="matrix">矩陣</param>
/// <returns>true：是對(duì)稱(chēng)矩陣 false：不是對(duì)稱(chēng)矩陣</returns>
private static bool isSymmetric(double[][] matrix)
{
 //矩陣沒(méi)有元素的情況
 if (matrix.Length == 0)
 {
  return true;
 }
 //合法性檢查：1）matrix應(yīng)為矩陣；2）matrix應(yīng)為方陣
 if (!isMatrix(matrix) || matrix.Length != matrix[0].Length)
 {
  throw new Exception("輸入不合法");
 }
 //矩陣對(duì)稱(chēng)條件：對(duì)任意i,j有a[i,j]=a[j,i]
 for (int i = 0; i < matrix.Length; i++)
 {
  for (int j = 0; j < i; j++)
  {
   if (matrix[i][j] != matrix[j][i])
   {
    return false;
   }
  }
 }
 return true;
}

2.判斷反稱(chēng)矩陣

對(duì)任意i和j，有a[i,j]=-a[j,i]

/// <summary>
/// 檢查一個(gè)矩陣是否為反稱(chēng)矩陣
/// </summary>
/// <param name="matrix">矩陣</param>
/// <returns>true：是反稱(chēng)矩陣 false：不是反稱(chēng)矩陣</returns>
private static bool isSkewSymmetric(double[][] matrix)
{
 //矩陣沒(méi)有元素的情況
 if (matrix.Length == 0)
 {
  return true;
 }
 //合法性檢查：1）matrix應(yīng)為矩陣；2）matrix應(yīng)為方陣
 if (!isMatrix(matrix) || matrix.Length != matrix[0].Length)
 {
  throw new Exception("輸入不合法");
 }
 //矩陣反稱(chēng)條件：對(duì)任意i,j有a[i,j]=-a[j,i]
 for (int i = 0; i < matrix.Length; i++)
 {
  for (int j = 0; j <= i; j++)
  {
   if (matrix[i][j] != -matrix[j][i])
   {
    return false;
   }
  }
 }
 return true;
}

3.相關(guān)函數(shù)

/// <summary>
/// 判斷一個(gè)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;
}

4.函數(shù)調(diào)用示例

1）Main函數(shù)代碼

static void Main(string[] args)
{
 //測(cè)試矩陣1：matrix1
 double[][] matrix1 = new double[][] 
 {
  new double[] { 1, 2, 3 },
  new double[] { 2, 1, 2 },
  new double[] { 3, 2, 1 }
 };
 if (isSymmetric(matrix1)) { Console.WriteLine("matrix1 是對(duì)稱(chēng)矩陣"); }
 else { Console.WriteLine("matrix1 不是對(duì)稱(chēng)矩陣"); }
 if (isSkewSymmetric(matrix1)) { Console.WriteLine("matrix1 是反稱(chēng)矩陣"); }
 else { Console.WriteLine("matrix1 不是反稱(chēng)矩陣"); }
 //測(cè)試矩陣2：matrix2
 double[][] matrix2 = new double[][] 
 {
  new double[] { 0, 1, 2 },
  new double[] { -1, 0, 1 },
  new double[] { -2, -1, 0 }
 };
 if (isSymmetric(matrix2)) { Console.WriteLine("matrix2 是對(duì)稱(chēng)矩陣"); }
 else { Console.WriteLine("matrix2 不是對(duì)稱(chēng)矩陣"); }
 if (isSkewSymmetric(matrix2)) { Console.WriteLine("matrix2 是反稱(chēng)矩陣"); }
 else { Console.WriteLine("matrix2 不是反稱(chēng)矩陣"); }
 //測(cè)試矩陣3：matrix3
 double[][] matrix3 = new double[][] 
 {
  new double[] { 1, 2, 3 },
  new double[] { 4, 5, 6 },
  new double[] { 7, 8, 9 }
 };
 if (isSymmetric(matrix3)) { Console.WriteLine("matrix3 是對(duì)稱(chēng)矩陣"); }
 else { Console.WriteLine("matrix3 不是對(duì)稱(chēng)矩陣"); }
 if (isSkewSymmetric(matrix3)) { Console.WriteLine("matrix3 是反稱(chēng)矩陣"); }
 else { Console.WriteLine("matrix3 不是反稱(chēng)矩陣"); }
 Console.ReadLine();
}

2）示例運(yùn)行結(jié)果