Function inv

numpy/linalg/linalg.py:493–562

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 -------

(a)

@array_function_dispatch(_unary_dispatcher)
def 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.

    See Also
    --------
    scipy.linalg.inv : Similar function in SciPy.

    Notes
    -----

    .. versionadded:: 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],