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Let T be a one-to-one and onto linear map of II to II. Suppose that (Тx — Ту,Тx — Ту) %3D (х — у,х — у) Vx,у € П. - Prove T is orthogonal. That is show a non-singular linear map which preserves distances is an orthogonal transformation.

Let T be a one-to-one and onto linear map of II to II. Suppose that (Тx — Ту,Тx — Ту) %3D (х — у,х — у) Vx,у € П. - Prove T is orthogonal. That is show a non-singular linear map which preserves distances is an orthogonal transformation.

Advanced Engineering Mathematics
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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Let T be a one-to-one and onto linear map of II to II. Suppose that (Тx — Ту,Тx — Ту) %3 (х — у, х — у) Vx,у € П. | Prove T is orthogonal. That is show a non-singular linear map which preserves distances is an orthogonal transformation.
Transcribed Image Text:Let T be a one-to-one and onto linear map of II to II. Suppose that (Тx — Ту,Тx — Ту) %3 (х — у, х — у) Vx,у € П. | Prove T is orthogonal. That is show a non-singular linear map which preserves distances is an orthogonal transformation.
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