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Prove Theorem 4.2.21. The Singular Value Decomposition. PROVE THAT IF MATRIX A element of R^n*n

Theorem 4.2.21. Let A e Rnxn. Then ||A|

Definition 4.2.2. On R we will use the standard inner product (7.7) = .2.2015 j=1

| 7 ||2=1 Theorem 4.2.20. Let A € RX. Then ||A||2 = 01. Proof: Let AE Rnxn and let Let A=USVT be an SVD of A. We have || A|

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Answer #1

Theorem 2,4121; A = paar The Wallip Proof: As we know by Theorem 2.4.20 R 11 All2=0, ie 11 Alla = max (7) Now Frobenius norm

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