An inequality for non-negative matrices. (English) Zbl 0930.15020
The article is concerned with vectors and matrices with non-negative entries.
Reviewer: Peter Reichensperger (Oberasbach)
MSC:
| 15A45 | Miscellaneous inequalities involving matrices |
| 15B48 | Positive matrices and their generalizations; cones of matrices |
References:
| [1] | Cobham, A., On the Hartmanis-Steams problem for a class of tag machines, (IEEE Conference Record of 1968 Ninth Annual Symposium on Switching and Automata Theory. IEEE Conference Record of 1968 Ninth Annual Symposium on Switching and Automata Theory, IBM Research Technical Report RC-2178 (August 23 1968)), also appeared as |
| [2] | Dulmage, A. L.; Mendelsohn, N. S., Gaps in the exponent set of primitive matrices, Illinois J. Math., 8, 642-656 (1964) · Zbl 0125.00706 |
| [3] | Gantmacher, F. R., The Theory of Matrices, vol. 2 (1974), Chelsea · Zbl 0085.01001 |
| [4] | Heap, B. R.; Lynn, M. S., The index of primitivity of a non-negative matrix, Numer. Math., 6, 120-141 (1964) · Zbl 0121.26303 |
| [5] | Heap, B. R.; Lynn, M. S., The structure of powers of nonnegative matrices I. The index of convergence, SIAM J. Appl. Math., 14, 610-639 (1966) · Zbl 0166.03705 |
| [6] | Heap, B. R.; Lynn, M. S., The structure of powers of nonnegative matrices II. The index of maximum density, SIAM J. Appl. Math., 14, 762-777 (1966) · Zbl 0166.03705 |
| [7] | Holladay, J. C.; Varga, R. S., On powers of non-negative matrices, (Proc. Amer. Math. Soc., 9 (1958)), 631-634 · Zbl 0096.00805 |
| [8] | Hopcroft, J. E.; Ullman, J. D., Introduction to Automata Theory, Languages, and Computation (1979), Addison-Wesley: Addison-Wesley Prague · Zbl 0196.01701 |
| [9] | Landau, E., Über die Maximalordnung der Permutationen gegebenen Grades, Archiv der Mathematik und Physik, 5, 92-103 (1903) · JFM 34.0233.02 |
| [10] | Marcus, M.; May, F., The maximum number of zeros in the powers of an indecomposable matrix, Duke Math. J., 29, 581-588 (1962) · Zbl 0201.36902 |
| [11] | Mařik, J.; Pták, V., Norms, spectra, and combinatorial properties of matrices, Czech. Math. J., 10, 181-196 (1960) · Zbl 0093.24205 |
| [12] | Massias, J.-P.; Nicolas, J.-L.; Robin, G., Effective bounds for the maximal order of an element in the symmetric group, Math. Comp., 53, 665-678 (1989) · Zbl 0675.10028 |
| [13] | Miller, W., The maximum order of an element of a finite symmetric group, Amer. Math. Monthly, 94, 497-506 (1987) · Zbl 1191.11027 |
| [14] | Minc, H., Nonnegative Matrices (1988), Wiley: Wiley Reading, MA · Zbl 0638.15008 |
| [15] | Perkins, P., A theorem on regular matrices, Pacific J. Math., 11, 1529-1533 (1961) · Zbl 0103.00801 |
| [16] | Pták, V., On a combinatorial theorem and its application to nonnegative matrices, Czech. Math. J., 8, 487-495 (1958), (in Russian, summary in English) · Zbl 0082.24402 |
| [17] | Pták, V.; Sedláček, J., On the index of imprimitivity of nonnegative matrices, Czech. Math. J., 8, 496-501 (1958), (in Russian, summary in English) · Zbl 0082.24403 |
| [18] | Pullman, N., On the number of positive entries in the powers of a non-negative matrix, Canad. Math. Bull., 7, 525-537 (1964) · Zbl 0143.26304 |
| [19] | Rosenblatt, D., On the graphs and asymptotic forms of finite boolean relation matrices and stochastic matrices, Naval Res. Logist. Quart., 4, 151-167 (1957) |
| [20] | Rozenberg, G.; Salomaa, A., (The Mathematical Theory of L Systems vol. 90, Pure and Applied Mathematics (1980), Academic Press: Academic Press New York) · Zbl 0365.68072 |
| [21] | Seneta, E., Non-negative Matrices (1973), George Allen & Unwin: George Allen & Unwin New York · Zbl 0278.15011 |
| [22] | Wielandt, H., Unzerlegbare, nicht negative Matrizen, Math. Zeitschift, 52, 642-648 (1950) · Zbl 0035.29101 |
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