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On the exponent of a primitive, nearly reducible matrix. II. (English) Zbl 0507.05013


MSC:

05B20 Combinatorial aspects of matrices (incidence, Hadamard, etc.)
05C50 Graphs and linear algebra (matrices, eigenvalues, etc.)
15A45 Miscellaneous inequalities involving matrices
05C20 Directed graphs (digraphs), tournaments

Citations:

Zbl 0436.05023
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Full Text: DOI

References:

[1] Berge, Claude, Graphs and hypergraphs, (1973) · Zbl 0254.05101
[2] Berman, Abraham; Plemmons, RobertJ., Nonnegative matrices in the mathematical sciences, (1979) · Zbl 0484.15016
[3] Brualdi, RichardA.; Hedrick, MarkB., A unified treatment of nearly reducible and nearly decomposable matrices, Linear Algebra Appl., 24, 51, (1979) · Zbl 0403.15008 · doi:10.1016/0024-3795(79)90146-0
[4] Brualdi, RichardA.; Ross, JeffreyA., On the exponent of a primitive, nearly reducible matrix, Math. Oper. Res., 5, 229, (1980) · Zbl 0436.05023
[5] Denardo, EricV., Periods of connected networks and powers of nonnegative matrices, Math. Oper. Res., 2, 20, (1977) · Zbl 0399.15011
[6] Dulmage, A. L.; Mendelsohn, N. S., Gaps in the exponent set of primitive matrices, Illinois J. Math., 8, 642, (1964) · Zbl 0125.00706
[7] Heap, B. R.; Lynn, M. S., The index of primitivity of a non-negative matrix, Numer. Math., 6, 120, (1964) · Zbl 0121.26303
[8] Holladay, JohnC.; Varga, RichardS., On powers of non-negative matrices, Proc. Amer. Math. Soc., 9, 631, (1958) · Zbl 0096.00805
[9] Kemeny, JohnG.; Snell, J. Laurie, Finite Markov chains, (1960) · Zbl 0089.13704
[10] Lewin, Mordechai, On exponents of primitive matrices, Numer. Math., 18, 154, (197172) · Zbl 0221.15021
[11] Lewin, Mordechai, Bounds for exponents of doubly stochastic primitive matrices, Math. Z., 137, 21, (1974) · Zbl 0276.15024
[12] Ross, J. A.; Lucchesi, C., Superfluous paths in strong digraphs, Discrete Math., 47, 267, (1983) · Zbl 0526.05028
[13] Varga, RichardS., Matrix iterative analysis, (1962)
[14] Wielandt, Helmut, Unzerlegbare, nicht negative matrizen, Math. Z., 52, 642, (1950) · Zbl 0035.29101
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