Unformatted text preview: | . Problem 3 (30 points) Prove Schwarz inequality for the inner product of two linear operators A and B : tr( A Â· A â€ ) Â· tr( B Â· B â€ ) â‰¥| tr( A Â· B â€ ) | 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 = Â± 0 1 1 0 Â¶ , S y = Â± 0 -i i Â¶ , S z = Â± 1 0 -1 Â¶ . Construct the commutators [ S x ,S y ] , [ S y ,S z ] and [ S z ,S x ]....
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- Fall '08
- Computer Science, Hilbert space, tensor product, Prove Schwarz Inequality