Izvorni znanstveni članak
A combinatorial method for determining the spectrum of the linear combinations of finitely many diagonalizable matrices that mutually commute
Emre Kişi
Halim Özdemir
Puni tekst: engleski pdf 220 Kb
str. 61-78
preuzimanja: 464
citiraj
APA 6th Edition
Kişi, E. i Özdemir, H. (2018). A combinatorial method for determining the spectrum of the linear combinations of finitely many diagonalizable matrices that mutually commute. Mathematical Communications, 23 (1), 61-78. Preuzeto s https://hrcak.srce.hr/192123
MLA 8th Edition
Kişi, Emre i Halim Özdemir. "A combinatorial method for determining the spectrum of the linear combinations of finitely many diagonalizable matrices that mutually commute." Mathematical Communications, vol. 23, br. 1, 2018, str. 61-78. https://hrcak.srce.hr/192123. Citirano 31.01.2025.
Chicago 17th Edition
Kişi, Emre i Halim Özdemir. "A combinatorial method for determining the spectrum of the linear combinations of finitely many diagonalizable matrices that mutually commute." Mathematical Communications 23, br. 1 (2018): 61-78. https://hrcak.srce.hr/192123
Harvard
Kişi, E., i Özdemir, H. (2018). 'A combinatorial method for determining the spectrum of the linear combinations of finitely many diagonalizable matrices that mutually commute', Mathematical Communications, 23(1), str. 61-78. Preuzeto s: https://hrcak.srce.hr/192123 (Datum pristupa: 31.01.2025.)
Vancouver
Kişi E, Özdemir H. A combinatorial method for determining the spectrum of the linear combinations of finitely many diagonalizable matrices that mutually commute. Mathematical Communications [Internet]. 2018 [pristupljeno 31.01.2025.];23(1):61-78. Dostupno na: https://hrcak.srce.hr/192123
IEEE
E. Kişi i H. Özdemir, "A combinatorial method for determining the spectrum of the linear combinations of finitely many diagonalizable matrices that mutually commute", Mathematical Communications, vol.23, br. 1, str. 61-78, 2018. [Online]. Dostupno na: https://hrcak.srce.hr/192123. [Citirano: 31.01.2025.]
Sažetak
et , , be diagonalizable matrices that mutually commute. This paper provides a combinatorial method to handle the problem of when a linear combination matrix is a matrix such that , where , , are nonzero complex scalars and denotes the spectrum of the matrix . If the spectra of the matrices and , , are chosen as subsets of some particular sets, then this problem is equivalent to the problem of characterizing all situations in which a linear combination of some commuting special types of matrices, e.g. the matrices such that , , is also a special type of matrix. The method developed in this note makes it possible to solve such characterization problems for the linear combinations of finitely many special types of matrices. Moreover, the method is illustrated by considering the problem, which is one of the open problems left in [Linear Algebra Appl. 437 (2012) 2091-2109], of characterizing all situations in which a linear combination is a tripotent matrix when is an involutory matrix and both and are tripotent matrices that mutually commute. The results obtained cover those established in the reference above.
Ključne riječi
Diagonalizable matrices; Commutativity; Spectrum; Linear combination; Systems of linear equations
Hrčak ID:
192123
URI
https://hrcak.srce.hr/192123
Datum izdavanja:
30.5.2018.
Posjeta: 1.141
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