(2) Let V be a finite-dimensional vector space and T E L(V). Suppose that T is diago- nalizable. Let A1,...,Am denote the distinct eigenvalues of T. Prove that (T – A11) - - - (T – AmI) = 0. %3D

Linear Algebra: A Modern Introduction
4th Edition
ISBN:9781285463247
Author:David Poole
Publisher:David Poole
Chapter7: Distance And Approximation
Section7.4: The Singular Value Decomposition
Problem 29EQ
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(2) Let V be a finite-dimensional vector space and T E L(V). Suppose that T is diago-
nalizable. Let A1,...,Am denote the distinct eigenvalues of T. Prove that
(T – A11) - - - (T – AmI) = 0.
%3D
Transcribed Image Text:(2) Let V be a finite-dimensional vector space and T E L(V). Suppose that T is diago- nalizable. Let A1,...,Am denote the distinct eigenvalues of T. Prove that (T – A11) - - - (T – AmI) = 0. %3D
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