Differential Equations Solutions 31

Differential Equations Solutions 31 - Chapter 8 Solutions:...

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Chapter 8 Solutions: Case Study: The Direction-of-Arrival Problem: Coming at You CHALLENGE 8.1. Let w k = SCz k , and multiply the equation BA Φ SCz k = λ k BASCz k by ( BA ) 1 to obtain Φ w k = λ k w k ,k =1 ,...,d. Then, by the defnition oF eigenvalue, we see that λ k is an eigenvalue oF Φ corre- sponding to the eigenvector w k . Since Φ is a diagonal matrix, its eigenvalues are its diagonal entries, so the result Follows. CHALLENGE 8.2. Using the SVD oF b U , we see that T [ U 1 U 2 ]= Δ V = · Δ · V 1 V 3 ¸ Δ · V 2 V 4 ¸¸ . Now we compute the matrices From Problem 1: BASC =[ Δ 1 1 , 0 d × ( m d ) ] T U 1 [ Σ 1 , 0 d × ( n
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This note was uploaded on 01/21/2012 for the course MAP 3302 taught by Professor Dr.robin during the Fall '11 term at University of Florida.

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