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Unformatted text preview: | . Problem 3 (30 points) Prove Schwarz inequality for the inner product of two linear operators A and B : tr( A A ) tr( B B ) | tr( A B ) | 2 Problem 4 (10 points) Show that A is Hermitian (self-adjoint) if and only if: A T = A * with A T the transpose of A and A * the complex conjugate of A . Problem 5 (20 points) Consider the following three matrices: S x = 0 1 1 0 , S y = 0 -i i , S z = 1 0 -1 . Construct the commutators [ S x ,S y ] , [ S y ,S z ] and [ S z ,S x ]....
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This note was uploaded on 08/08/2011 for the course COT 6600 taught by Professor Staff during the Fall '08 term at University of Central Florida.
- Fall '08
- Computer Science