26. Prove: If {u1, u2, . . . , u,} is an orthonormal basis for R", andif A can be expressed asA = c,u,u + c,u,u + · · + c,,4,U,then A is symmetric and has eigenvalues c1, C2, . . . , Cn .

Answered: Image /qna-images/answer/d6347280-6946-4f4b-8244-bd9cb84bdbe1.jpg

Answered: Prove: If {uj, u2, .. . , u,} is an…

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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Prove: If {uj, u2, .. . , u,} is an orthonormal basis for R", if A can be expressed as and "n "n"ɔ A = c,u,u + c,u,u +..+c,u,u then A is symmetric and has eigenvalues c1, C2, . . . , Cp. T