Let V be a finite-dimensional vector space, and let λ be any scalar.(a) For any ordered basis β for V, prove that [λIV]β= λ.(b) Compute the characteristic polynomial of λIV.(c) Show that λIV is diagonalizable and has only one eigenvalue.
Let V be a finite-dimensional vector space, and let λ be any scalar.(a) For any ordered basis β for V, prove that [λIV]β= λ.(b) Compute the characteristic polynomial of λIV.(c) Show that λIV is diagonalizable and has only one eigenvalue.
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 13EQ
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