Algorithm to find Determinant of a Matrix

The idea is to first convert the given matrix to echelon form and then take the product of the diagonal elements

def det(mat):
    if len(mat) != len(mat[0]):
        raise ArithmeticError("Parameter must be a square matrix")
    if len(mat) == 1:
        return mat[0]
    if len(mat) == 2:
        return mat[0][0]*mat[1][1]-mat[0][1]*mat[1][0]
    
    factor = 1.0
    
    # copying the contents of matrix in a seperate array
    x = [row[:] for row in mat]
    
    while len(x)>2:
        # in case the first element of the matrix is 0
        # we swap the row with another row whose first element is not 0
        if x[0][0] == 0.0:
            for i in range(len(x)):

                # if we find such a row, we swap it with the first row and the factor becomes -1
                if x[i][0] != 0:
                    for j in range(len(x)):
                        temp = x[i][j]
                        x[i][j] = x[0][j]
                        x[0][j] = temp
                    factor *= -1.0
                    break

                # if we reach the end of the matrix and still don't find a suitable row, we return 0
                if x[i][0] == 0 and i==len(x)-1:
                    return 0
        
        factor *= x[0][0]
        arr = []
        for i in range(1,len(x)):
            tempArr = []
            for j in range(1,len(x)):
                tempArr.append(x[i][j]-x[0][j]*x[i][0]/x[0][0])
            arr.append(tempArr[:])
        x = [row[:] for row in arr]
        
    # at the end of the loop the size of x is always 2, so we can directly compute the result
    return factor*(x[0][0]*x[1][1]-x[0][1]*x[1][0])

These are the matrices on which we will test the algorithm

mat1 = [
    [2.0,5.0,1.0],
    [0.0,3.0,2.0],
    [0.0,0.0,4.0]
]

mat2 = [
    [5.0,2.0,3.0,1.0],
    [7.0,6.0,4.0,2.0],
    [5.0,6.0,7.0,5.0],
    [5.0,7.0,9.0,7.0]
]

Driver Code

if __name__ == "__main__":    
    print(det(mat1))
    print(det(mat2))

24.0
16.0

Now we'll check if our calculations are correct, using numpy

import numpy as np

# converting into numpy array
nmat1 = np.array(mat1)
nmat2 = np.array(mat2)

# computing determinant
det1 = np.linalg.det(nmat1)
det2 = np.linalg.det(nmat2)
print(det1,det2)

23.999999999999993 15.999999999999913

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