Consider the inner product of the vector space of continuous functions C[0,1],
(f,g) = "∫" f(t)g(t)dt. Let f(t) = 1 and let g(t) = 1. Calculate the distance d(f, g) between the vectors f and g in this vector space.
Consider the inner product defined on the vector space of 2 x 2 matrices W2,2 that is defined by (A,B) := (11A11 + 12B12 + 21B21 + 22B22). Calculate the cosine of the angle between vectors C and D in this inner product space when C = [3 3] and D = [-2 -2].