/// <summary>
/// 求矩阵的逆矩阵
/// </summary>
/// <param name="matrix"></param>
/// <returns></returns>
public static double[][] InverseMatrix(double[][] matrix)
{
 //matrix必须为非空
 if (matrix == null || matrix.Length == 0)
 {
  return new double[][] { };
 }
 //matrix 必须为方阵
 int len = matrix.Length;
 for (int counter = 0; counter < matrix.Length; counter++)
 {
  if (matrix[counter].Length != len)
  {
   throw new Exception("matrix 必须为方阵");
  }
 }
 //计算矩阵行列式的值
 double dDeterminant = Determinant(matrix);
 if (Math.Abs(dDeterminant) <= 1E-6)
 {
  throw new Exception("矩阵不可逆");
 }
 //制作一个伴随矩阵大小的矩阵
 double[][] result = AdjointMatrix(matrix);
 //矩阵的每项除以矩阵行列式的值，即为所求
 for (int i = 0; i < matrix.Length; i++)
 {
  for (int j = 0; j < matrix.Length; j++)
  {
   result[i][j] = result[i][j] / dDeterminant;
  }
 }
 return result;
}
/// <summary>
/// 递归计算行列式的值
/// </summary>
/// <param name="matrix">矩阵</param>
/// <returns></returns>
public static double Determinant(double[][] matrix)
{
 //二阶及以下行列式直接计算
 if (matrix.Length == 0) return 0;
 else if (matrix.Length == 1) return matrix[0][0];
 else if (matrix.Length == 2)
 {
  return matrix[0][0] * matrix[1][1] - matrix[0][1] * matrix[1][0];
 }
 //对第一行使用“加边法”递归计算行列式的值
 double dSum = 0, dSign = 1;
 for (int i = 0; i < matrix.Length; i++)
 {
  double[][] matrixTemp = new double[matrix.Length - 1][];
  for (int count = 0; count < matrix.Length - 1; count++)
  {
   matrixTemp[count] = new double[matrix.Length - 1];
  }
  for (int j = 0; j < matrixTemp.Length; j++)
  {
   for (int k = 0; k < matrixTemp.Length; k++)
   {
    matrixTemp[j][k] = matrix[j + 1][k >= i ? k + 1 : k];
   }
  }
  dSum += (matrix[0][i] * dSign * Determinant(matrixTemp));
  dSign = dSign * -1;
 }
 return dSum;
}
/// <summary>
/// 计算方阵的伴随矩阵
/// </summary>
/// <param name="matrix">方阵</param>
/// <returns></returns>
public static double[][] AdjointMatrix(double [][] matrix)
{
 //制作一个伴随矩阵大小的矩阵
 double[][] result = new double[matrix.Length][];
 for (int i = 0; i < result.Length; i++)
 {
  result[i] = new double[matrix[i].Length];
 }
 //生成伴随矩阵
 for (int i = 0; i < result.Length; i++)
 {
  for (int j = 0; j < result.Length; j++)
  {
   //存储代数余子式的矩阵（行、列数都比原矩阵少1）
   double[][] temp = new double[result.Length - 1][];
   for (int k = 0; k < result.Length - 1; k++)
   {
    temp[k] = new double[result[k].Length - 1];
   }
   //生成代数余子式
   for (int x = 0; x < temp.Length; x++)
   {
    for (int y = 0; y < temp.Length; y++)
    {
     temp[x][y] = matrix[x < i ? x : x + 1][y < j ? y : y + 1];
    }
   }
   //Console.WriteLine("代数余子式:");
   //PrintMatrix(temp);
   result[j][i] = ((i + j) % 2 == 0 ? 1 : -1) * Determinant(temp);
  }
 }
 //Console.WriteLine("伴随矩阵：");
 //PrintMatrix(result);
 return result;
}
/// <summary>
/// 打印矩阵
/// </summary>
/// <param name="matrix">待打印矩阵</param>
private static void PrintMatrix(double[][] matrix, string title = "")
{
 //1.标题值为空则不显示标题
 if (!String.IsNullOrWhiteSpace(title))
 {
  Console.WriteLine(title);
 }
 //2.打印矩阵
 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();
 }
 //3.空行
 Console.WriteLine();
}

static void Main(string[] args)
{
 double[][] matrix = new double[][] 
 {
  new double[] { 1, 2, 3 }, 
  new double[] { 2, 2, 1 },
  new double[] { 3, 4, 3 } 
 };
 PrintMatrix(matrix, "原矩阵");
 PrintMatrix(AdjointMatrix(matrix), "伴随矩阵");
 Console.WriteLine("行列式的值为：" + Determinant(matrix) + '\n');
 PrintMatrix(InverseMatrix(matrix), "逆矩阵");
 Console.ReadLine();
}