Kunze Linear Algebra · Problem 8

Elementary Canonical Forms

Mathematics — Methods · nilpotent-commutator-operator

Problem

Let VV be the space of n×nn \times n matrices over a field FF, and let AA be a fixed n×nn \times n matrix over FF. Define a linear operator TT on VV by T(B)=AB−BAT(B) = AB - BA. Prove that if AA is a nilpotent matrix, then TT is a nilpotent operator.

Browse the problem library