Some rank equalities for finitely many tripotent matrices

Abstract

‎A rank equality is established for the sum of finitely many tripotent matrices via elementary block matrix operations‎. ‎Moreover‎, ‎by using this equality and Theorems 8 and 10 in [Chen M‎. ‎and et al‎. ‎On the open problem related to rank equalities for the sum of finitely many idempotent matrices and its applications‎, ‎The Scientific World Journal 2014 (2014)‎, ‎Article ID 702413‎, ‎7 pages‎.]‎, ‎some other rank equalities for tripotent matrices are given‎. ‎Furthermore‎, ‎we obtain several rank equalities related to some special types of matrices‎, ‎some of which are available in the literature‎, ‎from the results established‎.