The Semigroup Generated by the Similarity Class of a Singular Matrix
ClΓ©ment de Seguins Pazzis Β· Communications in Algebra Β· 2012
Let A be a singular matrix of M n (π), where π is an arbitrary field. Using canonical forms, we give a new proof that the sub-semigroup of ( n (π), Γ) generated by the similarity class of A is the set of matrices of M n (π) with a rank lesser than or equal to that of A.