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Unformatted text preview: Math 235 Assignment 9 Due: Wednesday, July 13th 1 —2
1. Let A = 3 0 . Find the maximum and minimum value of for a? E R2 subject
1 2 to the constraint = 1. 2. Find a Singular value decomposition of each of the following matrices. a) [.11 ﬂ 1 —4
b) —2 2
2 4
1 O 1
C) 1 1—1
—11 O
O 1 1 3. Let A be an m x n matrix. Prove that if {Z is a left singular vector of A, then 71 is an
eigenvector of AAT. 4. Suppose that A is an n X n matrix with a singular value decomposition A = U EVT.
Prove that I det Al is the product of the singular values of A. Use MATLAB to complete the following questions. You do not need to submit a printout of your work. Simply use MATLAB to solve the problems,
and submit written answers to the questions along with the rest of your assignment. Singular Value Decomposition Find the Singular Value Decomposition of the matrix 5 5 5 5 5 5
M NS _[5_ 1.5 j M
10 10 10 10 10 10
A: __2\/5 6% 4\/5 _4\/’5’ O 2J5“
5 5 5 5 5
5 5 5 i
«5 M” i— [ 45 45
5 5 5
7 7 7 __7 Z Z
5 2 2 2 2 2 Hint: Type help svd at the prompt and read the documentation. What are U, E, and V? ...
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This note was uploaded on 09/30/2011 for the course MATH 235 taught by Professor Celmin during the Spring '08 term at Waterloo.
 Spring '08
 CELMIN

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