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

Its a linear algebra math problem. The answer is certainly in your linear algebra text book or [here](https://en.wikipedia.org/wiki/Determinant): — Jabberwocky, Oct 20 '17 at 12:41
if you want to learn you better write your own code, this one is frankly speaking pretty useless as it works only for matrices with only one particular size (10x10) — 463035818_is_not_an_ai, Oct 20 '17 at 12:42
@tobi303 not quite, it works for matrices from 1x1 to 10x10. — Jabberwocky, Oct 20 '17 at 12:43
@MichaelWalz yes I also just realized that, but the way this is done is not very clever but rather wasteful — 463035818_is_not_an_ai, Oct 20 '17 at 12:44
@MichaelWalz agreed, there is lots of opportunity to learn how to avoid unnecessary complexity that comes from nesting loops and stuff ;) — 463035818_is_not_an_ai, Oct 20 '17 at 12:46
@TobiasWeimer ok, I didn't check, but the result in that case is trivial anyway — Jabberwocky, Oct 20 '17 at 12:51

Dorian Gray · Accepted Answer · 2017-10-20T12:53:18.307

0

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.

edited Oct 20 '17 at 12:53

answered Oct 20 '17 at 12:46

Dorian Gray

2,913
1
9
25

1

Thank you very much for your quick reply – Muclos Oct 20 '17 at 12:52

score 0 · Answer 2 · edited Oct 18 '21 at 05:12

0

The program uses a recursive function to create a submatrix and compute the determinant when the submatrix is 2x2.

When the program has the determinant of the submatrix it sums and subtracts it as you can see on Wikipedia page about determinant.

At the end, the recursive function returns the determinant of the complete matrix.

edited Oct 18 '21 at 05:12

TimeTravelPenguin

313
2
14

answered Oct 20 '17 at 12:46

Giovanni Lorenzini

26
4

1

Thank you very much for your quick reply – Muclos Oct 20 '17 at 12:52

Understanding of a specific function Determinant of a Matrix

2 Answers2