Deteminant of a matrix 行列式值

Deteminant of a matrix 

矩陣 A 是方陣(Square Matrix)時才會有行列式值，而其行列式是表為 A 或 det A，其運算之結果是一個純量(Scalar)，而非一個矩陣也不是一個向量。

// C program to find Deteminant of a matrix
#include<stdio.h>
#include<math.h>
 
// Dimension of input square matrix
#define N 2
 
// Function to get cofactor of mat[p][q] in temp[][]. n is current
// dimension of mat[][]
void getCofactor(int mat[N][N], int temp[N][N], int p, int q, int n)
{
    int i = 0, j = 0;
 
    // Looping for each element of the matrix
    for (int row = 0; row < n; row++)
    {
        for (int col = 0; col < n; col++)
        {
            //  Copying into temporary matrix only those element
            //  which are not in given row and column
            if (row != p && col != q)
            {
                temp[i][j++] = mat[row][col];
 
                // Row is filled, so increase row index and
                // reset col index
                if (j == n - 1)
                {
                    j = 0;
                    i++;
                }
            }
        }
    }
}
 
/* Recursive function for finding determinant of matrix.
   n is current dimension of mat[][]. */
int determinantOfMatrix(int mat[N][N], int n)
{
    int D = 0; // Initialize result
 
    //  Base case : if matrix contains single element
    if (n == 1)
        return mat[0][0];
 
    int temp[N][N]; // To store cofactors
 
    int sign = 1;  // To store sign multiplier
 
     // Iterate for each element of first row
    for (int f = 0; f < n; f++)
    {
        // Getting Cofactor of mat[0][f]
        getCofactor(mat, temp, 0, f, n);
        D += sign * mat[0][f] * determinantOfMatrix(temp, n - 1);
 
        // terms are to be added with alternate sign
        sign = -sign;
    }
 
    return D;
}
 
/* function for displaying the matrix */
void display(int mat[N][N], int row, int col)
{
    for (int i = 0; i < row; i++)
    {
        for (int j = 0; j < col; j++)
            printf("  %d", mat[i][j]);
        printf("n");
    }
}
 
// Driver program to test above functions
int main()
{
    /* int mat[N][N] = {{6, 1, 1},
                     {4, -2, 5},
                     {2, 8, 7}}; */
 
    /*int mat[N][N] = {{1, 0, 2, -1},
                     {3, 0, 0, 5},
                     {2, 1, 4, -3},
                     {1, 0, 5, 0}
                    }; */
 
    int mat[N][N] = {{1, 2},
                     {3, 2} };
   
    printf("Determinant of the matrix is : %d",
            determinantOfMatrix(mat, N));
    return 0;
}

輸出畫面
Determinant of the matrix is : -4