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
icon
Related questions
Question

Please solve as soon as possible

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.
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.
Expert Solution
steps

Step by step

Solved in 2 steps with 2 images

Blurred answer
Recommended textbooks for you
Advanced Engineering Mathematics
Advanced Engineering Mathematics
Advanced Math
ISBN:
9780470458365
Author:
Erwin Kreyszig
Publisher:
Wiley, John & Sons, Incorporated
Numerical Methods for Engineers
Numerical Methods for Engineers
Advanced Math
ISBN:
9780073397924
Author:
Steven C. Chapra Dr., Raymond P. Canale
Publisher:
McGraw-Hill Education
Introductory Mathematics for Engineering Applicat…
Introductory Mathematics for Engineering Applicat…
Advanced Math
ISBN:
9781118141809
Author:
Nathan Klingbeil
Publisher:
WILEY
Mathematics For Machine Technology
Mathematics For Machine Technology
Advanced Math
ISBN:
9781337798310
Author:
Peterson, John.
Publisher:
Cengage Learning,
Basic Technical Mathematics
Basic Technical Mathematics
Advanced Math
ISBN:
9780134437705
Author:
Washington
Publisher:
PEARSON
Topology
Topology
Advanced Math
ISBN:
9780134689517
Author:
Munkres, James R.
Publisher:
Pearson,