Original scientific paper
A combinatorial method for determining the spectrum of the linear combinations of finitely many diagonalizable matrices that mutually commute
Emre Kişi
Halim Özdemir
Full text: english pdf 220 Kb
page 61-78
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cite
APA 6th Edition
Kişi, E. & 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. Retrieved from https://hrcak.srce.hr/192123
MLA 8th Edition
Kişi, Emre and 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, no. 1, 2018, pp. 61-78. https://hrcak.srce.hr/192123. Accessed 23 Feb. 2025.
Chicago 17th Edition
Kişi, Emre and Halim Özdemir. "A combinatorial method for determining the spectrum of the linear combinations of finitely many diagonalizable matrices that mutually commute." Mathematical Communications 23, no. 1 (2018): 61-78. https://hrcak.srce.hr/192123
Harvard
Kişi, E., and 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), pp. 61-78. Available at: https://hrcak.srce.hr/192123 (Accessed 23 February 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 [cited 2025 February 23];23(1):61-78. Available from: https://hrcak.srce.hr/192123
IEEE
E. Kişi and 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, no. 1, pp. 61-78, 2018. [Online]. Available: https://hrcak.srce.hr/192123. [Accessed: 23 February 2025]
Abstract
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.
Keywords
Diagonalizable matrices; Commutativity; Spectrum; Linear combination; Systems of linear equations
Hrčak ID:
192123
URI
https://hrcak.srce.hr/192123
Publication date:
30.5.2018.
Visits: 1.186
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