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5. Let U: R →R be linear. Show that the following statements are equivalent: (a) U is an orthogonal matrix. (b) If {x¹,x²,...,x^} is an orthonormal basis of R", then the image set {U (x¹), U(x²),…..‚U(r)} is an orthonormal basis of R.

5. Let U: R →R be linear. Show that the following statements are equivalent: (a) U is an orthogonal matrix. (b) If {x¹,x²,...,x^} is an orthonormal basis of R", then the image set {U (x¹), U(x²),…..‚U(r)} is an orthonormal basis of R.

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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matrix analysis practice question,Please write the simplest answer process,thanks.
5. Let U: R → R be linear. Show that the following statements are equivalent: (a) U is an orthogonal matrix. (b) If {x¹,x²,...,x"} is an orthonormal basis of R", then the image set {U (x¹), U(x²),…..‚U(r)} is an orthonormal basis of R.
Transcribed Image Text:5. Let U: R → R be linear. Show that the following statements are equivalent: (a) U is an orthogonal matrix. (b) If {x¹,x²,...,x"} is an orthonormal basis of R", then the image set {U (x¹), U(x²),…..‚U(r)} is an orthonormal basis of R.
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