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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 definition 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 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
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