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Consider the following argument: let C E Rxn be such that CTC = CCT. Using the SVD we can write C = UZVT, and since CTC = CCT we see that v STUTUEV T = USV TV ΣUT and thus V ΣΤΣV T = UΣΣTUT. Therefore U = V and C is a symmetric matrix. Can you say something on the soundness of this argument with appropriate justifications?

Consider the following argument: let C E Rxn be such that CTC = CCT. Using the SVD we can write C = UZVT, and since CTC = CCT we see that v STUTUEV T = USV TV ΣUT and thus V ΣΤΣV T = UΣΣTUT. Therefore U = V and C is a symmetric matrix. Can you say something on the soundness of this argument with appropriate justifications?

Advanced Engineering Mathematics
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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Consider the following argument: let C E Rnxn be such that CTC = CCT. Using the SVD we can write C = UZVT, and since CTC = CCT we see that V ΣTUTUEV T = USV TV ΣUT and thus V ΣΤΣV T = UΣΣTUT . Therefore U = V and C is a symmetric matrix. Can you say something on the soundness of this argument with appropriate justifications?
Transcribed Image Text:Consider the following argument: let C E Rnxn be such that CTC = CCT. Using the SVD we can write C = UZVT, and since CTC = CCT we see that V ΣTUTUEV T = USV TV ΣUT and thus V ΣΤΣV T = UΣΣTUT . Therefore U = V and C is a symmetric matrix. Can you say something on the soundness of this argument with appropriate justifications?
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