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
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ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
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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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