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1 0 0 cos 0 sin i. Find the inverse of R. Show that R= 0 sin o cos is orthogonal. ii. Find the eigenvalues and the eigenvectors of R. Are the eigenvectors orthogonal? Note: Two complex vectors x and y are orthogonal means xªy = x¹y = 0 (xª is the hermitian transpose of x, i.e., the transpose of the complex conjugate of x).

1 0 0 cos 0 sin i. Find the inverse of R. Show that R= 0 sin o cos is orthogonal. ii. Find the eigenvalues and the eigenvectors of R. Are the eigenvectors orthogonal? Note: Two complex vectors x and y are orthogonal means xªy = x¹y = 0 (xª is the hermitian transpose of x, i.e., the transpose of the complex conjugate of x).

Advanced Engineering Mathematics
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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1 0 0 cos 0 sino i. Find the inverse of R. (b) Show that R = 0 sin o cos is orthogonal. ii. Find the eigenvalues and the eigenvectors of R. Are the eigenvectors orthogonal? Note: Two complex vectors x and y are orthogonal means xªy xTy - 0 (xH is the hermitian transpose of x, i.e., the transpose of the complex conjugate of x). =
Transcribed Image Text:1 0 0 cos 0 sino i. Find the inverse of R. (b) Show that R = 0 sin o cos is orthogonal. ii. Find the eigenvalues and the eigenvectors of R. Are the eigenvectors orthogonal? Note: Two complex vectors x and y are orthogonal means xªy xTy - 0 (xH is the hermitian transpose of x, i.e., the transpose of the complex conjugate of x). =
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