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Unformatted text preview: . Summarize your conclusion about the impact of the third equation, as a function of ǫ , on the LS solution. 2. Fat systems: Consider ˆ i , ˆ j , ˆ k as unit vectors in the x , y and z directions. (a) Consider the fat (under-specifed) system Ax = b b 1 2 ǫ 2-1-ǫ B x y z = b 1-1 B with ǫ a very small number. (a) Identify span( A ) and null( A )? (b) What can you say about the solution space? 3. Singular Value Decomposition (SVD) Let A = b 1 1 1-1 1 B and ²nd U , Σ and V such that A = U Σ V T . Repeat the process on A T . Use the fact that U = eig ( AA T ) ∈ R m × m and V = eig ( A T A ) ∈ R n × n , where eig ( S ) are the eigenvectors of a symmetric matrix S . Version 1.13 March 18, 2011 ˜ /493/Assignments/HW #3b – Version 1.13 March 18, 2011...
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This note was uploaded on 03/28/2011 for the course ECE ECE 493 taught by Professor Jontb.allen during the Spring '11 term at University of Illinois at Urbana–Champaign.
- Spring '11