The matrix has a singular value decomposition A = UEVT where and and The 3,2 entry of Vis (V)32 = -1/√√x. What is x? Answer: 3 A = -E -6 3 -6 -3 -6 0 6 1 √6 1 R1 * U = √6 0 12 0 0 Σ = 0 6 0 0 0 0 1 √6 1 √3 1 1 S-WIN si-si- 11011 √2

Linear Algebra: A Modern Introduction
4th Edition
ISBN:9781285463247
Author:David Poole
Publisher:David Poole
Chapter4: Eigenvalues And Eigenvectors
Section4.3: Eigenvalues And Eigenvectors Of N X N Matrices
Problem 28EQ
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The matrix
has a singular value decomposition A = UZVT where
and
and
The 3,2 entry of V is (V)32 = −1/√√x.
What is x?
Answer:
A =
U =
V =
*
*
*
Σ =
3
-6 -3
3 -6 -3
-6
0
6
-15-15-15
-|-|
-|-|S
√3
1
√6
1
√6
23
12 0
0
0
6
00 0
-SINS-
1
√2
√2
0
-S-S
1
√2
0
1
√x √2
Transcribed Image Text:The matrix has a singular value decomposition A = UZVT where and and The 3,2 entry of V is (V)32 = −1/√√x. What is x? Answer: A = U = V = * * * Σ = 3 -6 -3 3 -6 -3 -6 0 6 -15-15-15 -|-| -|-|S √3 1 √6 1 √6 23 12 0 0 0 6 00 0 -SINS- 1 √2 √2 0 -S-S 1 √2 0 1 √x √2
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