[8 3. Consider the matrix A = of Problem 1(a). Let o1, o2 be the singular values of A. (a) Find all singular value decompositions A = oju, v + ozu2v". (b) Find an orthonormal eigenbasis {v1, V2} of A" A such that A" Av; = o v; and an orthonormal eigenbasis {u1, u2} of AA" such that AA" u; = o?u;, such that A is not equal to oju,v{+o2u2v%. [Hint: The condition Av; = 0;u; is not automatic!

[8 3. Consider the matrix A = of Problem 1(a). Let o1, o2 be the singular values of A. (a) Find all singular value decompositions A = oju, v + ozu2v". (b) Find an orthonormal eigenbasis {v1, V2} of A" A such that A" Av; = o v; and an orthonormal eigenbasis {u1, u2} of AA" such that AA" u; = o?u;, such that A is not equal to oju,v{+o2u2v%. [Hint: The condition Av; = 0;u; is not automatic!

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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