h11-4 - { a } where a R is a member of the Borel sigma...

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COT5615 Mathematics for Intelligent Systems Fall 2011 Home Work Assignment 4: Due Wednesday 11/30/11 before class 1. Prove that if A is a square matrix (i.e., n × n ) then the eigen values of A T A and AA T are the same. 2. Prove that if A is an n × n real symmetric matrix, then det( A ) = Q n i =1 λ i where λ i is the i th eigen value of A . 3. Prove that the set of all rational numbers (and therefore the set of all irrational numbers) is a member of the Borel σ -algebra on R . Prove that the set comprising of any singleton element:
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Unformatted text preview: { a } where a R is a member of the Borel sigma algebra. 4. Derive the KullbackLeibler divergence between the two 1-dimensional Gaussian density functions f 1 ( x ) = 1 2 2 e-( x- 1 ) 2 2 2 and f 2 ( x ) = 1 2 2 e-( x- 2 ) 2 2 2 Note that the Gaussians differ only in their means and not their variances. 1...
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This note was uploaded on 01/22/2012 for the course COP 5615 taught by Professor Staff during the Fall '08 term at University of Florida.

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