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A semigroup treatment of some theorems on non-negative matrices. (English) Zbl 0232.20139


MSC:

15B48 Positive matrices and their generalizations; cones of matrices
20M99 Semigroups
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References:

[1] A. L. Dulmage N. S. Mendelsohn: The exponent of a primitive matrix. Canadian Math. Bull. 5 (1962), 241-244. · Zbl 0108.01203
[2] Ф. Р. Гантмахер: Теория матриц. Москва 1953. · Zbl 1151.94459
[3] K. L. Chung: Markov chains with stationary transition probabilities. Berlin 1960. · Zbl 0092.34304
[4] J. Mařík, Vl. Pták: Norms, spectra and combinatorial properties of matrices. Czechoslovak Math. J. 10 (85) (1960), 181-196. · Zbl 0093.24205
[5] Vl. Pták: Об одной комбинаторной теореме и ее применении к неотрицательным матрицам. Чех. мат. ж. 8 (83) (1958), 487-495.
[6] Vl. Pták I. Sedláček: Об индексе импримитивности неотрицательных матриц. Чех. мат. ж. 8 (83) (1958), 496-501.
[7] В. И. Романовский: Дискретные цепы Маркова. Москва 1949. · Zbl 1152.51302
[8] Š. Schwarz: Subsemigroups of simple semigroups. Czechoslovak Math. J. 13 (88) (1963), 226-239. · Zbl 0122.02402
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