Determines if a matrix is approximately orthogonal.

    A matrix is orthogonal if it's square and real and its transpose is its
    inverse.

    Args:
        matrix: The matrix to check.
        rtol: The per-matrix-entry relative tolerance on equality.
        atol: The per-matrix-entry absolute tolerance on equality.

    Returns:
        Whether the matrix is orthogonal within the given tolerance.

def is_orthogonal(
        matrix: np.ndarray,
        *,
        rtol: float = 1e-5,
        atol: float = 1e-8) -> bool:
    """Determines if a matrix is approximately orthogonal.

    A matrix is orthogonal if it's square and real and its transpose is its
    inverse.

    Args:
        matrix: The matrix to check.
        rtol: The per-matrix-entry relative tolerance on equality.
        atol: The per-matrix-entry absolute tolerance on equality.

    Returns:
        Whether the matrix is orthogonal within the given tolerance.
    """
    return (matrix.shape[0] == matrix.shape[1] and
            np.all(np.imag(matrix) == 0) and
            np.allclose(matrix.dot(matrix.T), np.eye(matrix.shape[0]),
                        rtol=rtol,
                        atol=atol))