Kunze Linear Algebra · Problem 6.4.13

Elementary Canonical Forms

Mathematics — Methods · left-multiplication-commutator-diagonalizable

Problem

Let VV be the space of n×nn \times n matrices over FF. Let AA be a fixed n×nn \times n matrix over FF. Let TT and UU be the linear operators on VV defined by T(B)=ABT(B) = AB U(B)=AB−BA.U(B) = AB - BA. (a) True or false? If AA is diagonalizable (over FF), then TT is diagonalizable. (b) True or false? If AA is diagonalizable, then UU is diagonalizable.

Browse the problem library