Let {u1,..., u„} be an orthonormal basis for R", and let21, ...,A, be any real scalars. DefineA = 2,u¡u{ + ... + d,u,ua. Show that A is symmetric.b. Show that 1, ..,A, are the eigenvalues of A.

According to the given information suppose that,

Answered: Let {u1,..., u„} be an orthonormal…

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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Let {u1,..., u„} be an orthonormal basis for R", and let 21, ...,A, be any real scalars. Define A = 2,u¡u{ + ... + d,u,u a. Show that A is symmetric. b. Show that 1, ..,A, are the eigenvalues of A.