7. Let u be a unit vector in Rn and define H = I - 2uu. Show that: (a) H is symmetric. (b) H is orthogonal. (c) H-¹ = H.
7. Let u be a unit vector in Rn and define H = I - 2uu. Show that: (a) H is symmetric. (b) H is orthogonal. (c) H-¹ = H.
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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q7
Transcribed Image Text:7. Let u be a unit vector in Rn and define H = I - 2uu. Show that:
(a) H is symmetric.
(b) H is orthogonal.
(c) H-¹ = H.
(d) Describe the geometric meaning of the linear operator on R" defined by H. (Hint: Com-
pute Hu and Hv for any v that is orthogonal to u.)
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