def cross_product_matrix(vec):
    """Returns a 3x3 cross-product matrix from a 3-element vector."""
    return np.array([[0, -vec[2], vec[1]],
                     [vec[2], 0, -vec[0]],
                     [-vec[1], vec[0], 0]])
Returns a 3x3 cross-product matrix from a 3-element vector.