21 Y1 Y2 C2 2. Recall that if x = and y are complex vectors, we define their : : an Yn inner product as (x,y) = x1y1 + x

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21 Y1 Y2 C2 2 Recall That If X And Y Are Complex Vectors We Define Their An Yn Inner Product As X Y X1y1 X 1 (41.69 KiB) Viewed 18 times

21 Y1 Y2 C2 2. Recall that if x = and y are complex vectors, we define their : : an Yn inner product as (x,y) = x1y1 + x212 + ... + xnyn. (1) ("") 4 1+ i (a) Let a = 1 and b i Calculate (a, b) and (b, a). (Do you 2 + 2i 5 get what you expected?) (b) Let x,y and z be complex vectors, all with n entries, and let a be a complex scalar. Prove the following: i. a(x, y) = (ax, y) ii. a(x,y) = (x, ay) iii. (x + y, z) = (x,z) + (y, z). = = =