Semigroups of linear endomorphisms closed under conjugation
João Araüjo, Fernando C. Silva · Communications in Algebra · 2000
Let a,b be singular endomorphisms of a. finite dimensional vector space V and denote by S a the semigroup generated by all the elements g -1ag, where gϵAut(V).The aim of this paper is to prove that bϵS a if and only if rank(b) ≥ rank(a).