(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.
Linear Algebra: A Modern Introduction
4th Edition
ISBN:9781285463247
Author:David Poole
Publisher:David Poole
Chapter5: Orthogonality
Section5.4: Orthogonal Diagonalization Of Symmetric Matrices
Problem 27EQ
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