def tests() -> None:
    a = np.array([[2, 2 + 1j, 4], [2 - 1j, 3, 1j], [4, -1j, 1]])
    v = np.array([[1], [2], [3]])
    assert is_hermitian(a), f"{a} is not hermitian."
    print(rayleigh_quotient(a, v))

    a = np.array([[1, 2, 4], [2, 3, -1], [4, -1, 1]])
    assert is_hermitian(a), f"{a} is not hermitian."
    assert rayleigh_quotient(a, v) == float(3)