求四阶矩阵的逆矩阵C语言代码

以下是求解4阶矩阵逆矩阵的C语言代码：

#include <stdio.h>

#define N 4

void printMatrix(float matrix[N][N]) {
    for (int i = 0; i < N; i++) {
        for (int j = 0; j < N; j++) {
            printf("%.2f ", matrix[i][j]);
        }
        printf("\n");
    }
}

void getCofactor(float matrix[N][N], float temp[N][N], int p, int q, int n) {
    int i = 0, j = 0;
    for (int row = 0; row < n; row++) {
        for (int col = 0; col < n; col++) {
            if (row != p && col != q) {
                temp[i][j++] = matrix[row][col];
                if (j == n - 1) {
                    j = 0;
                    i++;
                }
            }
        }
    }
}

float determinant(float matrix[N][N], int n) {
    float det = 0;
    if (n == 1) {
        return matrix[0][0];
    }
    float temp[N][N];
    int sign = 1;
    for (int i = 0; i < n; i++) {
        getCofactor(matrix, temp, 0, i, n);
        det += sign * matrix[0][i] * determinant(temp, n - 1);
        sign = -sign;
    }
    return det;
}

void adjoint(float matrix[N][N], float adj[N][N]) {
    if (N == 1) {
        adj[0][0] = 1;
        return;
    }
    int sign = 1;
    float temp[N][N];
    for (int i = 0; i < N; i++) {
        for (int j = 0; j < N; j++) {
            getCofactor(matrix, temp, i, j, N);
            sign = ((i + j) % 2 == 0) ? 1 : -1;
            adj[j][i] = sign * determinant(temp, N - 1);
        }
    }
}

int inverse(float matrix[N][N], float inv[N][N]) {
    float det = determinant(matrix, N);
    if (det == 0) {
        printf("Matrix is singular and has no inverse\n");
        return 0;
    }
    float adj[N][N];
    adjoint(matrix, adj);
    for (int i = 0; i < N; i++) {
        for (int j = 0; j < N; j++) {
            inv[i][j] = adj[i][j] / det;
        }
    }
    return 1;
}

int main() {
    float matrix[N][N] = {{1, 2, 3, 4}, {5, 6, 7, 8}, {9, 10, 11, 12}, {13, 14, 15, 16}};
    float inv[N][N];
    if (inverse(matrix, inv)) {
        printf("Inverse of the matrix:\n");
        printMatrix(inv);
    }
    return 0;
}

该代码实现了矩阵的求行列式、伴随矩阵、逆矩阵，其中逆矩阵的计算是通过将伴随矩阵除以行列式得到的。在 main 函数中，我们可以将需要求逆矩阵的矩阵存储在一个二维数组中，然后调用 inverse 函数来求解逆矩阵。如果矩阵是奇异的，即行列式为零，那么逆矩阵不存在。