V2 -V2 -V2/2 -1 /2/2 –1 1 -/2/2] V2/2 V2 1 A = 2 You should be able to complete each step by hand. (a) Find the eigenvalues of AT A, A1 2 12 2 A3 2 0.
V2 -V2 -V2/2 -1 /2/2 –1 1 -/2/2] V2/2 V2 1 A = 2 You should be able to complete each step by hand. (a) Find the eigenvalues of AT A, A1 2 12 2 A3 2 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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Question
![V2
-V2
-V2/2
V2/2 -1
1
1
A =
-1
You should be able to complete each step by hand.
(a) Find the eigenvalues of A" A, A1 > A2 > A3 2 0.
(b) Find a complete orthonormal set of eigenvectors {v1, v2, V3}, where v; is an eigen-
vector for Ai.
(c) Set up the 4 × 3 matrix E with Ei = 0; = VA; (the ith singular value) and all other
Eiji
= 0.
(d) Find u; the left singular vectors. Recall u; =
Av; for i = 1,2,3 and u4 is a basis
for NS(A").
(e) Let U = [ui u2
u3 u4] and V = [v1 v2 v3].
(f) Verify that A = UEVT.
This all works out very nicely for this carefully chosen matrix A.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F44e216e5-25df-4033-a49c-7e662c9a93ef%2Fa462c129-161b-4274-ba8e-f91af97a522c%2F2yot15m_processed.png&w=3840&q=75)
Transcribed Image Text:V2
-V2
-V2/2
V2/2 -1
1
1
A =
-1
You should be able to complete each step by hand.
(a) Find the eigenvalues of A" A, A1 > A2 > A3 2 0.
(b) Find a complete orthonormal set of eigenvectors {v1, v2, V3}, where v; is an eigen-
vector for Ai.
(c) Set up the 4 × 3 matrix E with Ei = 0; = VA; (the ith singular value) and all other
Eiji
= 0.
(d) Find u; the left singular vectors. Recall u; =
Av; for i = 1,2,3 and u4 is a basis
for NS(A").
(e) Let U = [ui u2
u3 u4] and V = [v1 v2 v3].
(f) Verify that A = UEVT.
This all works out very nicely for this carefully chosen matrix A.
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