let T be a linear operator on a finite- dimensional vector space V, and let f(t) be the characteristic polynomial of  T. then f(t)= to the zero transformation. that is, T "satisfies" its  characteristic equation.

Linear Algebra: A Modern Introduction
4th Edition
ISBN:9781285463247
Author:David Poole
Publisher:David Poole
Chapter6: Vector Spaces
Section6.6: The Matrix Of A Linear Transformation
Problem 43EQ
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let T be a linear operator on a finite-
dimensional vector space V, and let f(t) be the characteristic polynomial of 
T. then f(t)= to the zero transformation. that is, T "satisfies" its 
characteristic equation.

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