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Numpy linalg.det not returning the same value for the same matrix?

I made the following program:

import numpy as np

def rayleigh_quot(A,X):
    D = X.T @ A @ X
    Q = norme_euclid(X)**2
    return D/Q

def norme_euclid(M):
    M = np.array(M)
    return np.sqrt(np.max(np.linalg.eig(M@M.T)[0]))

def X_iter(A,X):
    D = A @ X
    Q = norme_euclid(A @ X)
    return (D/Q).reshape(3,1)

def is_invert(M):
    print(M)
    print(f"\ndeterminant : {np.linalg.det(M)}")
    if np.linalg.det(M) == 0: 
        return False
    return True

def rayleigh_iter(A,B):
    X = B
    n = 0
    while(True):
        n += 1;
        print(n)
        v = rayleigh_quot(A,X)[0]
        Y = A-v*np.identity(A.shape[0])
        if not is_invert(Y):
            return v, Y
        M = np.linalg.inv(Y)
        X = X_iter(M,X)

A = np.array([[1,2,3],[1,2,1],[3,2,1]])
B = np.array([[1],[1],[1]])
v,Y = rayleigh_iter(A,B)

In the exection you get this : (only showing the relvent part)

iter 7
matrix M :
[[-4.23606798  2.          3.        ]
 [ 1.         -3.23606798  1.        ]
 [ 3.          2.         -4.23606798]]

determinant of M : -8.997687189537842e-14

iter 8
matrix M :
[[-4.23606798  2.          3.        ]
 [ 1.         -3.23606798  1.        ]
 [ 3.          2.         -4.23606798]]

determinant of M : 0.0

so as you can see it's returning a different value For appearently the same Matrix, so what's going on, is it not printing all the decimal values ?



source https://stackoverflow.com/questions/74436781/numpy-linalg-det-not-returning-the-same-value-for-the-same-matrix

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