Let w E R3 be a fixed vector with ||w|| = 1 and let f : R³ → R³ be the linear transformation given by f(v) = v – 2(v · w)w. Let M be the standard matrix of f. Find two eigenvalues of M and show that M is diago- nalizable.
Let w E R3 be a fixed vector with ||w|| = 1 and let f : R³ → R³ be the linear transformation given by f(v) = v – 2(v · w)w. Let M be the standard matrix of f. Find two eigenvalues of M and show that M is diago- nalizable.
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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Question
![7. Let w E R³ be a fixed vector with ||w|| = 1 and let f : R³ → R³ be the linear transformation
given by
f(v) = v – 2(v . w)w.
|
Let M be the standard matrix of f. Find two eigenvalues of M and show that M is diago-
nalizable.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F5cfad234-a2c2-4215-85c9-d792d8016066%2F47cc2557-a4bf-46ad-b6bf-d9fda4908068%2Fwultptq9_processed.png&w=3840&q=75)
Transcribed Image Text:7. Let w E R³ be a fixed vector with ||w|| = 1 and let f : R³ → R³ be the linear transformation
given by
f(v) = v – 2(v . w)w.
|
Let M be the standard matrix of f. Find two eigenvalues of M and show that M is diago-
nalizable.
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