/// <summary>
/// 求一個矩陣的轉置矩陣
/// </summary>
/// <param name="matrix">矩陣</param>
/// <returns>轉置矩陣</returns>
private static double[][] MatrixTranspose(double[][] matrix)
{
 //合法性檢查
 if (!isMatrix(matrix))
 {
  throw new Exception("matrix 不是一個矩陣");
 }
 //矩陣中沒有元素的情況
 if (matrix.Length == 0)
 {
  return new double[][] { };
 }
 double[][] result = new double[matrix[0].Length][];
 for (int i = 0; i < result.Length; i++)
 {
  result[i] = new double[matrix.Length];
 }
 //新矩陣生成規(guī)則： b[i,j]=a[j,i]
 for (int i = 0; i < result.Length; i++)
 {
  for (int j = 0; j < result[0].Length; j++)
  {
   result[i][j] = matrix[j][i];
  }
 }
 return result;
}

/// <summary>
/// 判斷一個二維數組是否為矩陣
/// </summary>
/// <param name="matrix">二維數組</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;
  }
 }
 //各行列數相等，則是矩陣
 return true;
}
/// <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();
 }
}

static void Main(string[] args)
{
 double[][] matrix = new double[][] 
 {
  new double[] { 1, 2, 3, 4 },
  new double[] { 4, 5, 6, 7 },
  new double[] { 7, 8, 9, 10}
 };
 //打印矩陣
 PrintMatrix(matrix);
 Console.WriteLine();
 //打印轉置后矩陣
 PrintMatrix(MatrixTranspose(matrix));
 Console.WriteLine();
 Console.ReadLine();
}