def lemma_8_3_3(a, u, b, v):
    """
    Demonstrates that if u is orthogonal to v then for any scalars a, b it continues to be true
    :param a: scalar
    :param u: n vector
    :param b: scalar
    :param v: n vector
    :return: a^2 * ||u||^2 + b^2 * ||v||^2
    >>> u = list2vec([1, 0])
    >>> v = list2vec([0, 1])
    >>> a = 2
    >>> b = 3
    >>> result = lemma_8_3_3(a, u, b, v)
    >>> result[0] == result[1]
    True
    >>> u = list2vec([1, 1]) # not orthogonal
    >>> v = list2vec([0, 1])
    >>> a = 2
    >>> b = 3
    >>> result = lemma_8_3_3(a, u, b, v)
    >>> result[0] != result[1]
    True
    """
    # t1 = (a * u + b * v) * (a * u + b * v)
    t1 = sum([(a*u), (b*v)])
    t1 *= t1
    t2 = a**2 * ((u * u)**(1/2))**2 + b**2 * ((v * v)**(1/2))**2
    return t1, t2