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Unformatted text preview: ECE 580 / Math 587 SPRING 2011 Correspondence # 7 February 21, 2011 ASSIGNMENT 3 Reading Assignment: Text: Chp 3; Correspondence # 6. Recommended Reading: Curtain & Pritchard: Chp 4 (pp. 55-64), Chp 5 (pp. 75-84). Balakrishnan: Chapters 1 and 2. Liusternik & Sobolev: Chapter 2 (pp. 73-83). Advance Reading: Text: Chapter 4; Review probability theory and stochastic processes from any (graduate) text of your choice. Problems (to be handed in): Due Date: Thursday, March 3 . 21. Let H be the space of all m × m matrices with complex-valued entries, with addition and multiplication defined as the standard corresponding operations with matrices, and with a candidate inner product of two matrices A, B defined as ( A, B ) = Trace ( A T Q ¯ B ) where A T denotes the transpose of the matrix A ; ¯ B denotes the complex conjugate of B ; and Q ∈ H is a Hermitian positive-definite matrix, that is Q T = ¯ Q and Q has only positive real eigenvalues. Prove that ( A, B ) as defined above is an inner product on...
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- Spring '08
- Optimization, Trigraph, dt, Hilbert space