The semigroup generated by the similarity class of a singular matrix
  Let A be a singular matrix of M_n(K), where K is an arbitrary field. Using canonical forms, we give a new proof that the sub-semigroup of (M_n(K),x) generated by the similarity class of A is the set of matrices of M_n(K) with a rank lesser than or equal to that of A. 
Cl\'ement de Seguins Pazzis
math.RA