A singular value decomposition o

Elements Of Modern Algebra
8th Edition
ISBN:9781285463230
Author:Gilbert, Linda, Jimmie
Publisher:Gilbert, Linda, Jimmie
Chapter1: Fundamentals
Section1.6: Matrices
Problem 18E: Prove part b of Theorem 1.35. Theorem 1.35 Special Properties of Let be an arbitrary matrix...
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A singular value decomposition of a matrix A is as follows:
0.5
0.5
0.5
0.5] [10 0]
-0.5 0.5
0.6]
-0.6 0.8
-0.5
0.5
0.8
A =
-0.5 -0.5
0.5
0.5
0.5
-0.5 -0.5 0.5
1. Find the closest (with respect to the Frobenius norm) matrix of rank 1 to A.
A1 =
2. Find the Frobenius norm of A – A1.
||A – A1||F
Transcribed Image Text:A singular value decomposition of a matrix A is as follows: 0.5 0.5 0.5 0.5] [10 0] -0.5 0.5 0.6] -0.6 0.8 -0.5 0.5 0.8 A = -0.5 -0.5 0.5 0.5 0.5 -0.5 -0.5 0.5 1. Find the closest (with respect to the Frobenius norm) matrix of rank 1 to A. A1 = 2. Find the Frobenius norm of A – A1. ||A – A1||F
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