Let T: V → V be a linear operator whose characteristic polynomial is pT(x)=x2(x−1)3(x+2)2. Judge each item below as true or false. (A) If the minimal polynomial of T is pT(x) then [T]BB is diagonal for some basis B of V. (B) Let A be the matrix of T with respect to some basis of V. Then, A2(A−I)3(A+2I)2 ≠ 0.

Let T: V → V be a linear operator whose characteristic polynomial is pT(x)=x2(x−1)3(x+2)2. Judge each item below as true or false. (A) If the minimal polynomial of T is pT(x) then [T]BB is diagonal for some basis B of V. (B) Let A be the matrix of T with respect to some basis of V. Then, A2(A−I)3(A+2I)2 ≠ 0.

Linear Algebra: A Modern Introduction

4th Edition

ISBN:9781285463247

Author:David Poole

Publisher:David Poole

Chapter4: Eigenvalues And Eigenvectors

Section4.4: Similarity And Diagonalization

Problem 51EQ

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