Function eig

numpy/linalg/_linalg.py:1367–1510

Compute the eigenvalues and right eigenvectors of a square array. Parameters ---------- a : (..., M, M) array Matrices for which the eigenvalues and right eigenvectors will be computed Returns ------- A namedtuple with the following attributes: eig

(a)

@array_function_dispatch(_unary_dispatcher)
def eig(a):
    """
    Compute the eigenvalues and right eigenvectors of a square array.

    Parameters
    ----------
    a : (..., M, M) array
        Matrices for which the eigenvalues and right eigenvectors will
        be computed

    Returns
    -------
    A namedtuple with the following attributes:

    eigenvalues : (..., M) array
        The eigenvalues, each repeated according to its multiplicity.
        The eigenvalues are not necessarily ordered. The resulting
        array will be of complex type, unless the imaginary part is
        zero in which case it will be cast to a real type. When `a`
        is real the resulting eigenvalues will be real (0 imaginary
        part) or occur in conjugate pairs

    eigenvectors : (..., M, M) array
        The normalized (unit "length") eigenvectors, such that the
        column ``eigenvectors[:,i]`` is the eigenvector corresponding to the
        eigenvalue ``eigenvalues[i]``.

    Raises
    ------
    LinAlgError
        If the eigenvalue computation does not converge.

    See Also
    --------
    eigvals : eigenvalues of a non-symmetric array.
    eigh : eigenvalues and eigenvectors of a real symmetric or complex
           Hermitian (conjugate symmetric) array.
    eigvalsh : eigenvalues of a real symmetric or complex Hermitian
               (conjugate symmetric) array.
    scipy.linalg.eig : Similar function in SciPy that also solves the
                       generalized eigenvalue problem.
    scipy.linalg.schur : Best choice for unitary and other non-Hermitian
                         normal matrices.

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

    This is implemented using the ``_geev`` LAPACK routines which compute
    the eigenvalues and eigenvectors of general square arrays.

    The number `w` is an eigenvalue of `a` if there exists a vector `v` such
    that ``a @ v = w * v``. Thus, the arrays `a`, `eigenvalues`, and
    `eigenvectors` satisfy the equations ``a @ eigenvectors[:,i] =
    eigenvalues[i] * eigenvectors[:,i]`` for :math:`i \\in \\{0,...,M-1\\}`.

    The array `eigenvectors` may not be of maximum rank, that is, some of the