행렬의 기저와 차원을 구하는 C++ 프로그램입니다.
알고리즘
Begin Function determinant() : It calculates determinant of the matrix. /* Arguments: n = number of elements. matrix[10][10] = input matrix. */ declare the submatrix submatrix[10][10]. //Body of the function: if (n == 2) return ((matrix[0][0] * matrix[1][1]) - (matrix[1][0] * matrix[0][1])) else Make a for loop c = 0 to n-1 Declare and initialize submati = 0, submatj. Make a For loop i = 1 to n-1 initialize subj = 0 Make a For loop i = 1 to n-1 if (j == c) continue submatrix[submati][submatj] = matrix[i][j]. Increment subj. increment submati. Compute d = d + (pow(-1, c) * matrix[0][c] * determinant(n- 1, submatrix)). End
예시
#include<iostream>
#include<math.h>
using namespace std;
double d = 0;
double determinant(int n, double matrix[10][10]) {
double submatrix[10][10];
if (n == 2)
return ((matrix[0][0] * matrix[1][1]) - (matrix[1][0] *
matrix[0][1]));
else {
for (int c = 0; c < n; c++) {
int submati = 0,submatj;
for (int i = 1; i < n; i++) {
int subj = 0;
for (int j = 0; j < n; j++) {
if (j == c)
continue;
submatrix[submati][submatj] = matrix[i][j];
subj++;
}
submati++;
}
d = d + (pow(-1, c) * matrix[0][c] * determinant(n -
1, submatrix));
}
}
return d;
}
int main(int argc, char **argv) {
cout << "Enter the number of elements:\n";
int n;
cin >> n;
double matrix[10][10];
cout << "Enter elements one by one:\n";
for (int i = 0; i < n; i++) {
for (int j = 0; j < n; j++) {
cin >> matrix[j][i];
}
}
d = determinant(n, matrix); //call the function
if (d != 0)
cout << "The elements form the basis of R" << n << " as the determinant is non-zero";
else
cout << "The elements don't form the basis of R" << n << " as the determinant is zero";
} 출력 - 1
Enter the number of elements: 3 Enter elements one by one: 7 6 1 2 3 4 5 8 9 The elements form the basis of R3 as the determinant is non-zero
출력 - 2
Enter the number of elements: 4 Enter the elements one by one: 7 6 1 4 2 3 5 4 9 8 2 3 2 1 3 0 The elements don't form the basis of R4 as the determinant is zero