SciPy

numpy.linalg.det

numpy.linalg.det(a)[source]

Compute the determinant of an array.

Parameters :

a : (..., M, M) array_like

Input array to compute determinants for.

Returns :

det : (...) array_like

Determinant of a.

See also

slogdet
Another way to representing the determinant, more suitable for large matrices where underflow/overflow may occur.

Notes

Broadcasting rules apply, see the numpy.linalg documentation for details.

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

Examples

The determinant of a 2-D array [[a, b], [c, d]] is ad - bc:

>>> a = np.array([[1, 2], [3, 4]])
>>> np.linalg.det(a)
-2.0

Computing determinants for a stack of matrices:

>>> a = np.array([ [[1, 2], [3, 4]], [[1, 2], [2, 1]], [[1, 3], [3, 1]] ])
>>> a.shape
(2, 2, 2
>>> np.linalg.det(a)
array([-2., -3., -8.])

Previous topic

numpy.linalg.cond

Next topic

numpy.linalg.matrix_rank