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(7) Suppose Q is a matrix with orthonormal columns. (a) Show that multiplication by Q preserves length; that is, ||Q'|| = ||7|| for any ĩ. (b) Suppose i is an eigenvector for Q; that is, a nonzero vector satisfying Qa = cĩ for some scalar c. Show that c=±1.

(7) Suppose Q is a matrix with orthonormal columns. (a) Show that multiplication by Q preserves length; that is, ||Q'|| = ||7|| for any ĩ. (b) Suppose i is an eigenvector for Q; that is, a nonzero vector satisfying Qa = cĩ for some scalar c. Show that c=±1.

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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(7) Suppose Q is a matrix with orthonormal columns. (a) Show that multiplication by Q preserves length; that is, ||QT|| = ||F|| for any i. (b) Suppose 7 is an eigenvector for Q; that is, a nonzero vector satisfying Qữ = ca for some scalar c. Show that c=±1.
Transcribed Image Text:(7) Suppose Q is a matrix with orthonormal columns. (a) Show that multiplication by Q preserves length; that is, ||QT|| = ||F|| for any i. (b) Suppose 7 is an eigenvector for Q; that is, a nonzero vector satisfying Qữ = ca for some scalar c. Show that c=±1.
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