tut11 - H T is Hermitian. 4: Prove that if U is unitary,...

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Math 235 Tutorial 11 Problems 1: Prove that ( A + B ) * = A * + B * and ( A - 1 ) * = ( A * ) - 1 . 2: Which of the following matrices are unitary, Hermitian, or both? a) A = ± 1 / 2 - 1 / 2 1 / 2 1 / 2 ² b) B = ± 1 / 2 - i/ 2 i/ 2 1 / 2 ² c) C = 1 / 3 0 1 / 3 - 1 / 3 1 / 3 2 / 6 - 1 / 3 0 - 1 / 3 1 / 6 0 - 1 / 3 0 1 / 6 1 / 3 1 / 3 . 3: Prove that if U is unitary and H is Hermitian, then U T is unitary and
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Unformatted text preview: H T is Hermitian. 4: Prove that if U is unitary, then | det U | = 1. Give an example where det U is not equal to 1 or -1. 5: What can you say about the eigenvalues of a matrix which is both unitary and Her-mitian? 1...
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This note was uploaded on 11/28/2011 for the course MATH 235 taught by Professor Celmin during the Fall '08 term at Waterloo.

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