Semigroup of generalized inverses of matrices
Hanifa Zekraoui · 2010
The paper is divided into two principal parts. In the flrst one, we give the set of generalized inverses of a matrix A a structure of a semigroup and study some algebraic properties like factorization and commutativity. We also deflne an equivalence relation in order to estab- lish an isomorphism between the quotient semigroup and the semigroup of projectors on R(A). In the second part, we study a relation between semigroups associated to equivalent matrices and establish a correspon- dence between the set of matrices and the set of associated semigroups. We also study some algebraic properties in this set like intersection and partial order.