Function is_hermitian

linear_algebra/src/rayleigh_quotient.py:10–27

Checks if a matrix is Hermitian. >>> import numpy as np >>> A = np.array([ ... [2, 2+1j, 4], ... [2-1j, 3, 1j], ... [4, -1j, 1]]) >>> is_hermitian(A) True >>> A = np.array([ ... [2, 2+1j, 4+1j], ... [2-1j, 3, 1j], ... [4, -1j, 1]])

(matrix: np.ndarray)

def is_hermitian(matrix: np.ndarray) -> bool:
    """
    Checks if a matrix is Hermitian.
    >>> import numpy as np
    >>> A = np.array([
    ... [2,    2+1j, 4],
    ... [2-1j,  3,  1j],
    ... [4,    -1j,  1]])
    >>> is_hermitian(A)
    True
    >>> A = np.array([
    ... [2,    2+1j, 4+1j],
    ... [2-1j,  3,  1j],
    ... [4,    -1j,  1]])
    >>> is_hermitian(A)
    False
    """
    return np.array_equal(matrix, matrix.conjugate().T)


def rayleigh_quotient(a: np.ndarray, v: np.ndarray) -> Any: