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.

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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