6. Decide if cach statement is true or false, and expalin why. (a) The left singular vectors of A are cigenvectors of A"A and the right singular vectors are eigen- vectors of AA". (b) For any matrix A, the matrices AA" and ATA have the same nonzero eigenvalues. (e) If S is symmetric, then the nonzero eigenvalues of S are its singular values. (d) IHA does not have full column rank, then 0 is a singular value of A. (e) Suppose that A is invertible with singular values o...,oa. Then for e2 0, the singular values of A+ cl, are o, + e,...+c. (f) The right singular vectors of A are orthogonal to Nul(A).

6. Decide if cach statement is true or false, and expalin why. (a) The left singular vectors of A are cigenvectors of A"A and the right singular vectors are eigen- vectors of AA". (b) For any matrix A, the matrices AA" and ATA have the same nonzero eigenvalues. (e) If S is symmetric, then the nonzero eigenvalues of S are its singular values. (d) IHA does not have full column rank, then 0 is a singular value of A. (e) Suppose that A is invertible with singular values o...,oa. Then for e2 0, the singular values of A+ cl, are o, + e,...+c. (f) The right singular vectors of A are orthogonal to Nul(A).

Linear Algebra: A Modern Introduction

4th Edition

ISBN:9781285463247

Author:David Poole

Publisher:David Poole

Chapter7: Distance And Approximation

Section7.4: The Singular Value Decomposition

Problem 59EQ

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