Rank equalities for commutator of generalized quadratic matrices and their applications

摘要

In this paper, rank equalities for commutator of generalized quadratic matrices are given by applying the mutual determined relationship between generalized quadratic matrices and idempotent ones. As applications, some rank equalities for commutator of scalar-potent matrices and scalar-involutory ones are obtained and the application ranges of rank equalities for commutator of idempotent matrices obtained by Tian, Y., Styan, G.P.H are extended to a more general state as well.