b) Consider an N x N matrix A with N orthonormal eigenvectors xi such that Axi = λi xi , where the λi is the eigenvalue corrosponding to eigenvector xi . It can be shown that such a matrix A has an expansion of the form : (see image) i) Show that if the eigenvalues are real then A , as defined through the above expansion , is Hermitian

b) Consider an N x N matrix A with N orthonormal eigenvectors xi such that Axi = λi xi , where the λi is the eigenvalue corrosponding to eigenvector xi . It can be shown that such a matrix A has an expansion of the form : (see image) i) Show that if the eigenvalues are real then A , as defined through the above expansion , is Hermitian

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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