numpy.linalg.det

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 represent the determinant, more suitable for large matrices where underflow/overflow may occur.

scipy.linalg.det

Similar function in SciPy.

Notes

New in version 1.8.0.

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 # may vary

Computing determinants for a stack of matrices:

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