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The Nullity, Rank, and Invertibility of Linear Combinations of k-Potent Matrices
dc.creator | Tošić, Marina | |
dc.creator | Ljajko, Eugen | |
dc.creator | Kontrec, Nataša | |
dc.creator | Stojanović, Vladica | |
dc.date.accessioned | 2024-02-27T13:09:47Z | |
dc.date.available | 2024-02-27T13:09:47Z | |
dc.date.issued | 2020 | |
dc.identifier.issn | 2227-7390 | |
dc.identifier.uri | https://jakov.kpu.edu.rs/handle/123456789/1635 | |
dc.description.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. | sr |
dc.language.iso | en | sr |
dc.publisher | Basel : MDPI | sr |
dc.rights | restrictedAccess | sr |
dc.source | Mathematics | sr |
dc.subject | k-potent matrix | sr |
dc.subject | linear combination | sr |
dc.subject | nonsingularity | sr |
dc.subject | rank | sr |
dc.subject | nullity | sr |
dc.title | The Nullity, Rank, and Invertibility of Linear Combinations of k-Potent Matrices | sr |
dc.type | article | sr |
dc.rights.license | ARR | sr |
dc.citation.volume | 8 | |
dc.citation.issue | 12 | |
dc.citation.spage | 2147 | |
dc.identifier.doi | 10.3390/math8122147 | |
dc.type.version | publishedVersion | sr |