numpy.linalg.inv()

numpy.linalg.inv(a) [source]

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:

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.

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]],
       [[-5. ,  2. ],
        [ 3. , -1. ]]])

Links:

https://docs.scipy.org/doc/numpy-1.11.0/reference/generated/numpy.linalg.inv.html

doc_NumPy

2025-01-10 15:47:30

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