def is_special_unitary(
        matrix: np.ndarray,
        *,
        rtol: float = 1e-5,
        atol: float = 1e-8) -> bool:
    """Determines if a matrix is approximately unitary with unit determinant.

    A matrix is special-unitary if it is square and its adjoint is its inverse
    and its determinant is one.

    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 unitary with unit determinant within the given
        tolerance.
    """
    return (is_unitary(matrix, rtol=rtol, atol=atol) and
            (matrix.shape[0] == 0 or
             np.allclose(np.linalg.det(matrix), 1, rtol=rtol, atol=atol)))