TY  - JOUR
AU  - Tošić, Marina
AU  - Ljajko, Eugen
AU  - Kontrec, Nataša
AU  - Stojanović, Vladica
PY  - 2020
UR  - https://jakov.kpu.edu.rs/handle/123456789/1635
AB  - 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.
PB  - Basel : MDPI
T2  - Mathematics
T1  - The Nullity, Rank, and Invertibility of Linear Combinations of k-Potent Matrices
VL  - 8
IS  - 12
SP  - 2147
DO  - 10.3390/math8122147
ER  - 

@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"
}

Tošić, M., Ljajko, E., Kontrec, N.,& Stojanović, V.. (2020). The Nullity, Rank, and Invertibility of Linear Combinations of k-Potent Matrices. in Mathematics
Basel : MDPI., 8(12), 2147.
https://doi.org/10.3390/math8122147

Tošić M, Ljajko E, Kontrec N, Stojanović V. The Nullity, Rank, and Invertibility of Linear Combinations of k-Potent Matrices. in Mathematics. 2020;8(12):2147.
doi:10.3390/math8122147 .

Tošić, Marina, Ljajko, Eugen, Kontrec, Nataša, Stojanović, Vladica, "The Nullity, Rank, and Invertibility of Linear Combinations of k-Potent Matrices" in Mathematics, 8, no. 12 (2020):2147,
https://doi.org/10.3390/math8122147 . .