from sage.all import *

def is_positive_semidefinite_naive(A):
    r"""
    A naive positive-semidefinite check that tests the eigenvalues for
    nonnegativity.  We follow the sage convention that positive
    (semi)definite matrices must be symmetric or Hermitian.

    SETUP::

        sage: from mjo.ldlt import is_positive_semidefinite_naive

    TESTS:

    The trivial matrix is vaciously positive-semidefinite::

        sage: A = matrix(QQ, 0)
        sage: A
        []
        sage: is_positive_semidefinite_naive(A)
        True

    """
    if A.nrows() == 0:
        return True # vacuously
    return A.is_hermitian() and all( v >= 0 for v in A.eigenvalues() )