Consider the matrix [2 3 A = (a) Find the Singular Value Decomposition (*SVD") of A. (Remember that the singular values must be listed in decreasing order in E.) (b) Assume that B is an n x n real matrix and its SVD is B = UEV*. Prove that VEV* is the square root of B*B. (Hint: compare B*B with (VEV*)².) (c) Using B = U£V* in part (b), Set S = (you do not have to prove these 2 facts). Use this and your SVD in part (a) to find the Polar Decomposition of A. UV*; we see that S is an isometry and VDV* is positive
Consider the matrix [2 3 A = (a) Find the Singular Value Decomposition (*SVD") of A. (Remember that the singular values must be listed in decreasing order in E.) (b) Assume that B is an n x n real matrix and its SVD is B = UEV*. Prove that VEV* is the square root of B*B. (Hint: compare B*B with (VEV*)².) (c) Using B = U£V* in part (b), Set S = (you do not have to prove these 2 facts). Use this and your SVD in part (a) to find the Polar Decomposition of A. UV*; we see that S is an isometry and VDV* is positive
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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![3. Consider the matrix
2 3
A
(a) Find the Singular Value Decomposition ("SVD") of A. (Remember that the singular values must
be listed in decreasing order in E.)
(b) Assume that B is an n x n real matrix and its SVD is B = UEV*. Prove that VEV* is the square
root of B* B. (Hint: compare B*B with (VEV*)².)
(c) Using B
(you do not have to prove these 2 facts). Use this and your SVD in part (a) to find the Polar
Decomposition of A.
: UEV* in part (b), Set S = UV*; we see that S is an isometry and VE* is positive](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F7abbf2d5-6ef3-489c-b2da-4d9327a88b2a%2F91073fb6-1c87-427d-8137-413604f4daa4%2Fk4hrkxw_processed.png&w=3840&q=75)
Transcribed Image Text:3. Consider the matrix
2 3
A
(a) Find the Singular Value Decomposition ("SVD") of A. (Remember that the singular values must
be listed in decreasing order in E.)
(b) Assume that B is an n x n real matrix and its SVD is B = UEV*. Prove that VEV* is the square
root of B* B. (Hint: compare B*B with (VEV*)².)
(c) Using B
(you do not have to prove these 2 facts). Use this and your SVD in part (a) to find the Polar
Decomposition of A.
: UEV* in part (b), Set S = UV*; we see that S is an isometry and VE* is positive
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