How to calculate the determinant of a matrix NxN ? [Recursively]

Question

I've been searching in all over the internet for an algorithm to calculate the determinant of NxN martix recursively . (I do not have any idea about the dimension, so N can be every integer that is less than 256)

complex<double> Matrix::matrixDeterminant(complex<double> **matrix, int n) {

  complex<double> det(0,0);

  complex<double> **submatrix;
  submatrix[i] =  new complex<double>[n]


  for(int i = 0; i< n; i++) {
      submatrix[i] = new complex<double>[n];
    }


   if (n == 2)
      return ((matrix[0][0] * matrix[1][1]) - (matrix[1][0] * matrix[0][1]));
   else {
      for (int x = 0; x < n; x++) {
            int subi = 0;
            for (int i = 1; i < n; i++) {
               int subj = 0;
               for (int j = 0; j < n; j++) {
                  if (j == x)
                  continue;
                  submatrix[subi][subj] = matrix[i][j];
                  subj++;
               }
               subi++;
            }
            det = det + (pow(-1, x) * matrix[0][x] * matrixDeterminant(submatrix, n - 1 ));
      }

   }
     return det;
}

as you can see, the matrix is a Complex matrix which is all the numbers inside are Complex numbers, and also returns complex number.

This method doesn't work. any ideas what to change to make it works?

Answer 1

Use Sarrus' Rule (non recursive method) example on below link is in Javascript, but easily can be written in C https://github.com/apanasara/Faster_nxn_Determinant

nxn Determinant computation thru only two loops