# HW2-sol - ECE 493 Univ of Illinois HW#2 Version 1.00 Due...

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ECE 493 HW #2 – Version 1.00 March 15, 2011 Spring 2011 Univ. of Illinois Due Thur, Mar. 10 Prof. Allen Topic of this homework: LinearAlgebra(Cauchy Schwartz inequality for n dimensional space. Eigenvalues and eigenvectors) Deliverables: Show your work. Numerical results are not suFcient expect when speci±cally requested. 1. Prove the Cauchy Schwartz inequality by following the argument below. (a) Use the argument based on the proof on pages 424-426 in the text book. Let V, U, E ( a ) be vectors in R n and a is a real scalar. Taking the norm of the error E ( a ) gives || E ( a ) || = || V - aU || . ²ind the minimum of E with respect to a . As shown in the book, use this to prove the CS inequality (13) page 424. Solution: In class I developed the Projection Thm which says that magnitude error of E ( a ) is minimum in length when E ( a * ) U , making a right triangle between V , the scaled U ( a * U ) and the error vector E ( a * ) = V - a * U . The *

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HW2-sol - ECE 493 Univ of Illinois HW#2 Version 1.00 Due...

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