A = 0 1 0 101 010 Consider an Nx N matrix A with N orthonormal eigenvectors x' such that Ax' = x¹, where the X, is the eigenvalue corresponding to eigenvector x'. It can be shown that such a matrix A has an expansion of the form: A=ΣA|x) (x²|=Ax(x¹)". i) Show that if the eigenvalues are real then A, as defined through the above expansion, is Hermitian.

A = 0 1 0 101 010 Consider an Nx N matrix A with N orthonormal eigenvectors x' such that Ax' = x¹, where the X, is the eigenvalue corresponding to eigenvector x'. It can be shown that such a matrix A has an expansion of the form: A=ΣA|x) (x²|=Ax(x¹)". i) Show that if the eigenvalues are real then A, as defined through the above expansion, is Hermitian.

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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