numpy.linalg.inv

numpy.linalg.inv(a)

Compute the (multiplicative) inverse of a matrix.

Given a square matrix a, return the matrix ainv satisfying dot(a, ainv) = dot(ainv, a) = eye(a.shape[0]).

Parameters:

a : (…, M, M) array_like

Matrix to be inverted.

Returns:

ainv : (…, M, M) ndarray or matrix

(Multiplicative) inverse of the matrix a.

Raises:

LinAlgError

If a is not square or inversion fails.

Notes

New in version 1.8.0.

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

Examples

>>> from numpy.linalg import inv
>>> a = np.array([[1., 2.], [3., 4.]])
>>> ainv = inv(a)
>>> np.allclose(np.dot(a, ainv), np.eye(2))
True
>>> np.allclose(np.dot(ainv, a), np.eye(2))
True

If a is a matrix object, then the return value is a matrix as well:

>>> ainv = inv(np.matrix(a))
>>> ainv
matrix([[-2. ,  1. ],
        [ 1.5, -0.5]])

Inverses of several matrices can be computed at once:

>>> a = np.array([[[1., 2.], [3., 4.]], [[1, 3], [3, 5]]])
>>> inv(a)
array([[[-2.  ,  1.  ],
        [ 1.5 , -0.5 ]],
       [[-1.25,  0.75],
        [ 0.75, -0.25]]])