Prove that a symmetric matrix has real eigenvalues and that the eigenvectors corresponding to distinct eigenvalues are mutually orthogonal. Use this fact to prove that any symmetric matrix A can be spectrally decomposed into CDC’ with D a diagonal matrix containing the eigenvalues and C the normalized eigenvectors arranged column-wise.

Prove that a symmetric matrix has real eigenvalues and that the eigenvectors corresponding to distinct eigenvalues are mutually orthogonal. Use this fact to prove that any symmetric matrix A can be spectrally decomposed into CDC’ with D a diagonal matrix containing the eigenvalues and C the normalized eigenvectors arranged column-wise.

Linear Algebra: A Modern Introduction

4th Edition

ISBN:9781285463247

Author:David Poole

Publisher:David Poole

Chapter7: Distance And Approximation

Section7.1: Inner Product Spaces

Problem 11AEXP

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