Given the matrix A = -1 1 -1 0-2 1 2 0 1 (a) Find the singular values o, of A. [Hint: first show that the characteristic polynomial of (AT A) is X³ – 13 X²+36 X.]
Given the matrix A = -1 1 -1 0-2 1 2 0 1 (a) Find the singular values o, of A. [Hint: first show that the characteristic polynomial of (AT A) is X³ – 13 X²+36 X.]
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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Question
![-1
1
-1
Given the matrix A =
0 -2
1
1
(a) Find the singular values o; of A.
[Hint: first show that the characteristic polynomial of (AT A) is X3 – 13 X2 + 36 A.]
(b) Find the rank 1 matrix A' that is closest to A (with respect to the Frobenius
norm). Note: you do NOT need to find the whole SVD to do this. Find only
those parts you need for A'.
(c) Find both the Frobenius norm ||A||F and the 2-norm ||A||2 of A.
Note: the matrix 2-norm is subordinate to the vector 2-norm.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F7701ebcd-ae79-49a5-aa56-eff1f72328a6%2F25f7d0c6-cd2d-4ddb-b66b-d894aadd5124%2Fmjgor5p_processed.jpeg&w=3840&q=75)
Transcribed Image Text:-1
1
-1
Given the matrix A =
0 -2
1
1
(a) Find the singular values o; of A.
[Hint: first show that the characteristic polynomial of (AT A) is X3 – 13 X2 + 36 A.]
(b) Find the rank 1 matrix A' that is closest to A (with respect to the Frobenius
norm). Note: you do NOT need to find the whole SVD to do this. Find only
those parts you need for A'.
(c) Find both the Frobenius norm ||A||F and the 2-norm ||A||2 of A.
Note: the matrix 2-norm is subordinate to the vector 2-norm.
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