Function inv

numpy/linalg/_linalg.py:548–660

Compute the inverse of a matrix. Given a square matrix `a`, return the matrix `ainv` satisfying ``a @ ainv = ainv @ a = eye(a.shape[0])``. Parameters ---------- a : (..., M, M) array_like Matrix to be inverted. Returns ------- ainv : (..., M, M) ndarra

(a)

@array_function_dispatch(_unary_dispatcher)
def inv(a):
    """
    Compute the inverse of a matrix.

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

    Parameters
    ----------
    a : (..., M, M) array_like
        Matrix to be inverted.

    Returns
    -------
    ainv : (..., M, M) ndarray or matrix
        Inverse of the matrix `a`.

    Raises
    ------
    LinAlgError
        If `a` is not square or inversion fails.

    See Also
    --------
    scipy.linalg.inv : Similar function in SciPy.
    numpy.linalg.cond : Compute the condition number of a matrix.
    numpy.linalg.svd : Compute the singular value decomposition of a matrix.

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

    If `a` is detected to be singular, a `LinAlgError` is raised. If `a` is
    ill-conditioned, a `LinAlgError` may or may not be raised, and results may
    be inaccurate due to floating-point errors.

    References
    ----------
    .. [1] Wikipedia, "Condition number",
           https://en.wikipedia.org/wiki/Condition_number

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