practice_problems2 - University of Michigan Fall 2011...

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University of Michigan Fall 2011 EECS551: Practice Problems 2 Instructor: Sandeep Pradhan 1 State TRUE or FALSE by giving reasons. If you give no reason or a wrong reason, you may not get credit. The eigen values of matrix b 5 4 2 5 B are 1 and 10. The eigen value of a projection matrix is either 1 or 1. Consider a Hilbert space X of dimension n . Let { p 1 ,..., p m } be a collection of linearly independent vectors in X . Consider an m × m matrix A , where its ( ij )th entry is given by a p i , p j A . Then the eigen values of A are non-negative. Let Q = b 1 0 . 5 0 . 5 1 B . The maximum value of x T Q x such that x T x = 1 is 2. Let S denote the space of all complex valued random variables. Consider the following function f : S × S → R , f ( X,Y ) = E (5 X * Y ) , where * denotes complex conjugation. This is a valid inner product. Consider an n × n complex-valued matrix A that satis±es A = A H . The eigenvalues of A are non-negative. 2 Let X denote the set of complex-valued CT signals de±ned on the interval [
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This note was uploaded on 01/10/2012 for the course EECS eecs551 taught by Professor J during the Spring '11 term at University of Michigan.

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