Abstract
The Frobenius form of an irreducible bistochastic matrix is clarified. A generalization of the Frobenius form for irreducible semigroups of bistochastic matrices is described.
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REFERENCES
Gantmacher F.R. Theory of matrices (Fizmatlit, Moscow, 2004) [in Russian].
Al'pin Yu.A. Nonnegative matrices (Kazansk. Fed. Univ., Kazan, 2015) [in Russian].
Paparella P. "Frobenius normal forms of doubly stochastic matrices", Spec. Matrices 7 (1), 213-217 (2019).
Protasov V.Yu., Voynov A.S. "Sets of nonnegative matrices without positive products", Linear Algebra Appl. 437 (3), 749-765 (2012).
Al'pin Yu.A., Al'pina V.S. "Combinatorial Properties of Entire Semigroups of Nonnegative Matrices", J. Math. Sci. 207, 674-685 (2015).
Sachkov V.N., Tarakanov V.E. Combinatorics of nonnegative matrices (Izd-vo TVP, Moscow, 2000) [in Russian].
Funding
The work of the first author is conducted in the framework of realization of the development programme of the Volga Region Scientific-Educational Center of Mathematics of Kazan (Volga region) Federal University, agreement no. 075-02-2020-1478.
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Communicated by M. M. Arslanov.
Russian Text © The Author(s), 2021, published in Izvestiya Vysshikh Uchebnykh Zavedenii. Matematika, 2021, No. 9, pp. 80–85.
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Al’pin, Y.A., Tregubov, V.G. Combinatorial Structure of a Semigroup of Bistochastic Matrices. Russ Math. 65, 69–72 (2021). https://doi.org/10.3103/S1066369X21090085
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DOI: https://doi.org/10.3103/S1066369X21090085