scipy.linalg.det#

scipy.linalg.det(a, overwrite_a=False, check_finite=True)[source]#

Compute the determinant of a matrix

The determinant of a square matrix is a value derived arithmetically from the coefficients of the matrix.

The determinant for a 3x3 matrix, for example, is computed as follows:

a    b    c
d    e    f = A
g    h    i

det(A) = a*e*i + b*f*g + c*d*h - c*e*g - b*d*i - a*f*h

Parameters:

a(M, M) array_like: A square matrix.
overwrite_abool, optional: Allow overwriting data in a (may enhance performance).
check_finitebool, optional: Whether to check that the input matrix contains only finite numbers. Disabling may give a performance gain, but may result in problems (crashes, non-termination) if the inputs do contain infinities or NaNs.

Returns:

detfloat or complex: Determinant of a.

Notes

The determinant is computed via LU factorization, LAPACK routine z/dgetrf.

Examples

>>> import numpy as np
>>> from scipy import linalg
>>> a = np.array([[1,2,3], [4,5,6], [7,8,9]])
>>> linalg.det(a)
0.0
>>> a = np.array([[0,2,3], [4,5,6], [7,8,9]])
>>> linalg.det(a)
3.0