@article{
author = "Tošić, Marina and Ljajko, Eugen and Kontrec, Nataša and Stojanović, Vladica",
year = "2020",
abstract = "Baksalary et al. (Linear Algebra Appl., doi:10.1016/j.laa.2004.02.025, 2004) investigated the invertibility of a linear combination of idempotent matrices. This result was improved by Koliha et al. (Linear Algebra Appl., doi:10.1016/j.laa.2006.01.011, 2006) by showing that the rank of a linear combination of two idempotents is constant. In this paper, we consider similar problems for k-potent matrices. We study the rank and the nullity of a linear combination of two commuting k-potent matrices. Furthermore, the problem of the nonsingularity of linear combinations of two or three k-potent matrices is considered under some conditions. In these situations, we derive explicit formulae of their inverses.",
publisher = "Basel : MDPI",
journal = "Mathematics",
title = "The Nullity, Rank, and Invertibility of Linear Combinations of k-Potent Matrices",
volume = "8",
number = "12",
pages = "2147",
doi = "10.3390/math8122147"
}