onsider a matrix A with N orthonormal eigenvectors {xi} and eigenvalues {λi}. Construct the matrix S from the eigenvectors of A as S = [x1 x2 · · · xN], where each column of S is an eigenvector of A. Because S is constructed from a set of linearly independent vectors, the inverse matrix S−1 exists. State the general condition on A for it to have a set of N orthonormal eigenvectors.

onsider a matrix A with N orthonormal eigenvectors {xi} and eigenvalues {λi}. Construct the matrix S from the eigenvectors of A as S = [x1 x2 · · · xN], where each column of S is an eigenvector of A. Because S is constructed from a set of linearly independent vectors, the inverse matrix S−1 exists. State the general condition on A for it to have a set of N orthonormal eigenvectors.

Linear Algebra: A Modern Introduction

4th Edition

ISBN:9781285463247

Author:David Poole

Publisher:David Poole

Chapter4: Eigenvalues And Eigenvectors

Section4.1: Introduction To Eigenvalues And Eigenvectors

Problem 36EQ: Consider again the matrix A in Exercise 35. Give conditions on a, b, c, and d such that A has two...

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