45. Let {v, w} be an orthonormal basis for R², and let T: R2 → R² be the function defined by T(u) = (u • v cos 0 +u•w sin0)v +(-u•v sin0 +u•wcos 0)w. Prove that T is an orthogonal operator.
45. Let {v, w} be an orthonormal basis for R², and let T: R2 → R² be the function defined by T(u) = (u • v cos 0 +u•w sin0)v +(-u•v sin0 +u•wcos 0)w. Prove that T is an orthogonal operator.
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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![45. Let {v, w} be an orthonormal basis for R², and let
T: R² → R² be the function defined by
T (u) = (u • v cos 0 +u•wsin0)v
+(-u•v sin0 +u•w cos 0)w.
Prove that T is an orthogonal operator.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F4bba3fcc-01db-410a-a86c-d766584e6d07%2F97682c91-2175-4edc-a65f-c3c5de591e83%2Fc8etunr_processed.png&w=3840&q=75)
Transcribed Image Text:45. Let {v, w} be an orthonormal basis for R², and let
T: R² → R² be the function defined by
T (u) = (u • v cos 0 +u•wsin0)v
+(-u•v sin0 +u•w cos 0)w.
Prove that T is an orthogonal operator.
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