Consider the n x n symmetric matrix H = I - 2uuT, where u is a unit vector in Rn, i.e., uTu = 1. (a) Show that H is an orthogonal matrix. (b) Show that u is an eigenvector of H and find the corresponding eigenvalue.
Consider the n x n symmetric matrix H = I - 2uuT, where u is a unit vector in Rn, i.e., uTu = 1. (a) Show that H is an orthogonal matrix. (b) Show that u is an eigenvector of H and find the corresponding eigenvalue.
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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Consider the n x n
(a) Show that H is an orthogonal matrix.
(b) Show that u is an eigenvector of H and find the corresponding eigenvalue.
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Step 1
(b) the corresponding Eigen value is (-1)
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