@article{article_680775, title={Alternative characterizations of some linear combinations of an idempotent matrix and a tripotent matrix that commute}, journal={Balıkesir Üniversitesi Fen Bilimleri Enstitüsü Dergisi}, volume={22}, pages={255–268}, year={2020}, DOI={10.25092/baunfbed.680775}, author={Petik, Tuğba and Gökmen, Burak Tufan}, keywords={Idempotent matrix,tripotent matrix,linear combination,commutativity}, abstract={In this work, first, Theorem 2 in [1] [Yao, H., Sun, Y., Xu, C., and Bu, C., A note on linear combinations of an idempotent matrix and a tripotent matrix, J. Appl. Math. Informatics, 27 (5-6), 1493-1499, 2009] and Theorem 2.2 in [2][Özdemir H., Sarduvan M., Özban A.Y., Güler N., On idempotency and tripotency of linear combinations of two commuting tripotent matrices, Appl. Math. Comput., 207 (1), 197-201, 2009] are reconsidered in different ways under the condition that the matrices involved in the linear combination are commutative. Thus, it is seen that there are some missing results in Theorem 2 in [1]. Then, by considering the obtained results and doing some detailed investigations, it is given a new characterization, without any restriction on the involved matrices except for commutativity, of a linear combination of an idempotent and a tripotent matrix that commute.}, number={1}, publisher={Balıkesir University}