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 : array_like, shape (M, M)

Matrix to be inverted.

Returns :

ainv : ndarray or matrix, shape (M, M)

(Multiplicative) inverse of the matrix a.

Raises :

LinAlgError :

If a is singular or not square.

Examples

>>> from numpy import linalg as LA
>>> a = np.array([[1., 2.], [3., 4.]])
>>> ainv = LA.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 = LA.inv(np.matrix(a))
>>> ainv
matrix([[-2. ,  1. ],
        [ 1.5, -0.5]])