python – Why does numpy calculate matrix determinant incorrectly

Question:

import numpy as np


A = np.array([[1, 1, 2, -1],
              [2, -1, 0, -5],
              [-1, -1, 0, -2],
              [6, 3, 4, -3]])

print(np.linalg.det(A))

I think so. The determinant must be equal to zero, I checked on a piece of paper and in online calculators. But this code gives such an answer 5.329070518200744e-15 . What am I doing wrong? Maybe he was inattentive somewhere, and if not, how is it better to calculate?

Answer:

I suppose it may depend only on the versions of Python and especially Numpy . In Google Colaboratory , exactly 0.0 comes out, even if you print 64 decimal places. I tried to set a different data type (the default in this matrix is numpy.int64 ), for example numpy.int16 or numpy.float32 – it doesn't matter, it still comes out 0.0 . But numpy.float16 cannot be set, linalg swears at it that it does not work with it. But check out for fun what type of data you get in the matrix:

print(type(A[0,0]))

In Google Colaboratory , these versions are:

Python 3.6.9
Numpy 1.18.5

The code I tested everything with:

import numpy as np

A = np.array([[1, 1, 2, -1],
              [2, -1, 0, -5],
              [-1, -1, 0, -2],
              [6, 3, 4, -3]] #, dtype=np.float32)
            )

print(np.__version__)
print(type(A[0,0]))  
print(np.linalg.det(A))
print(f"{np.linalg.det(A):.64f}")

Result:

1.18.5
<class 'numpy.int64'>
0.0
0.0000000000000000000000000000000000000000000000000000000000000000