Let u R3 be a unit vector. (a) Explain why the elementary reflection matrix R =

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Let u ˆˆ R3 be a unit vector.
(a) Explain why the elementary reflection matrix R = I - 2uuT represents a reflection through the plane orthogonal to u.
(b) Prove that R is an orthogonal matrix. Is it proper or improper?
(c) Write out R when u =

(d) Give a geometrical explanation why Qn = - R represents the rotation of Exercise 7.2.20.

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Applied Linear Algebra

ISBN: 978-0131473829

1st edition

Authors: Peter J. Olver, Cheri Shakiban

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Question Posted: Jun 17, 2016 09:00 AM

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Let u R3 be a unit vector. (a) Explain why the elementary reflection matrix R =

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(i) (3.0,-/ (ii) (iii) ( -**)" (급4 .-12)" 13' 13"13

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a First w u v u u T v u uu T v is the orthogonal projection of v onto th...View the full answer

Applied Linear Algebra

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