singular value decomposition of a matrix -0.5 0.5 0.5 -0.5] [10 0.5 0.5 0.5 0.5 0 -0.5 -0.5 0.5 0.5 0 0.5 -0.5 0.5 -0.5 0
singular value decomposition of a matrix -0.5 0.5 0.5 -0.5] [10 0.5 0.5 0.5 0.5 0 -0.5 -0.5 0.5 0.5 0 0.5 -0.5 0.5 -0.5 0
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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![A singular value decomposition of a matrix A is as follows:
-0.5 0.5 0.5 -0.5] [100]
0.5
0.5 0.5
0.5
0 5 0.6 0.8
-0.8 0.6
-0.5
-0.5 0.5
0.5
0 0
0.5
-0.5 0.5 -0.5 0 0
1. Find the closest (with respect to the Frobenius norm) matrix of rank 1 to A.
A =
=
A1 =
2. Find the Frobenius norm of A - A1.
||A - A1|| F =](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F9a5158e8-8b77-4b4e-8179-076b9d754f54%2Fb979ed30-6b50-4c7e-94f1-25d033ce33a8%2F61aa6j_processed.jpeg&w=3840&q=75)
Transcribed Image Text:A singular value decomposition of a matrix A is as follows:
-0.5 0.5 0.5 -0.5] [100]
0.5
0.5 0.5
0.5
0 5 0.6 0.8
-0.8 0.6
-0.5
-0.5 0.5
0.5
0 0
0.5
-0.5 0.5 -0.5 0 0
1. Find the closest (with respect to the Frobenius norm) matrix of rank 1 to A.
A =
=
A1 =
2. Find the Frobenius norm of A - A1.
||A - A1|| F =
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