Understanding of a specific function Determinant of a Matrix

Question

I have found a program on internet which calculate the determinant of a Matrix:

 /*
 * C++ Program to Find the Determinant of a Given Matrix
 */
#include<iostream>
#include<math.h>
#include<conio.h>
using namespace std;
double d = 0;
double det(int n, double mat[10][10])
{
    int c, subi, i, j, subj;
    double submat[10][10];  
    if (n == 2) 
    {
        return( (mat[0][0] * mat[1][1]) - (mat[1][0] * mat[0][1]));
    }
    else
    {  
        for(c = 0; c < n; c++)
        {  
            subi = 0;  
            for(i = 1; i < n; i++)
            {  
                subj = 0;
                for(j = 0; j < n; j++)
                {    
                    if (j == c)
                    {
                        continue;
                    }
                    submat[subi][subj] = mat[i][j];
                    subj++;
                }
                subi++;
            }
        d = d + (pow(-1 ,c) * mat[0][c] * det(n - 1 ,submat));
        }
    }
    return d;
}
int main()
{
    int n;
    cout<<"enter the order of matrix" ;
    cin>>n;
    double mat[10][10];
    int i, j;
    cout<<"enter the elements"<<endl;
    for(i=0;i<n;i++)
    {
        for(j=0;j<n;j++)
        {
            cin>>mat[i][j];
        }
    }
    cout<<"\ndeterminant"<<det(n,mat);
    getch();
}

source: http://www.sanfoundry.com/cpp-program-find-determinant-given-matrix/

I wanted to learn from it but i don't understand it. Is it any link with Gauss elimination? Otherwise do you know which process use this algorithm?

Thank you in advance to any one who may be able to help me

Answer 1

This is an algorithm which uses Lapace expansions, which recursively computes the determinant of an n x n matrix by computing n determinants of (n-1) x (n-1) subminors. The determinant of the 2 x 2 matrix should be obvious.

There are better ways to do that, like LU decomposition.