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The index of primitivity of a non-negative matrix

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References

  1. Berge, C.: The theory of graphs. London: Methuen, 1962.

    Google Scholar 

  2. Brauer, A.: On a problem of partitions. Amer. J. Math.64, 299–312 (1942).

    Google Scholar 

  3. —, andB. M. Seelbinder: On a problem of partitions II. Amer. J. Math.76, 343–346 (1954).

    Google Scholar 

  4. —, andJ. E. Shockley: On a problem of Frobenius. J. Reine Angew. Math.211, 215–220 (1962).

    Google Scholar 

  5. Debreu, G., andI. N. Herstein: Nonnegative square matrices. Econometrica21, 597–607 (1953).

    Google Scholar 

  6. Dulmage, A. L., andN. S. Mendelsohn: The exponent of a primitive matrix. Canad. Math. Bull.5, 241–244 (1962).

    Google Scholar 

  7. Frobenius, G.: Über Matrizen aus nicht negativen Elementen. S.-B. Preuss. Akad. Wiss. Berlin, 456–477 (1912).

    Google Scholar 

  8. Herstein, I. N.: A note on primitive matrices. Amer. Math. Monthly61, 18–20 (1954).

    Google Scholar 

  9. Holladay, J. C., andR. S. Varga: On powers of non-negative matrices. Proc. Amer. Math. Soc.9, 631–634 (1958).

    Google Scholar 

  10. Mařík, J., andV. Pták: Norms, spectra and combinatorial properties of matrices. Czechoslovak Math. J.10, 181–196 (1960).

    Google Scholar 

  11. Pták, V.: On a combinatorial theorem and its application to non-negative matrices. Czechoslovak Math. J.8, 487–495 (1958).

    Google Scholar 

  12. Rosenblatt, D.: On the graphs and asymptotic forms of finite Boolean relation matrices and stochastic matrices. Naval. Res. Logist. Quart.4, 151–167 (1957).

    Google Scholar 

  13. Varga, R. S.: Matrix iterative analysis. New Jersey: Prentice-Hall, 1962.

    Google Scholar 

  14. Warshall, S.: A theorem on Boolean matrices. J.A.C.M.9, 11–12 (1962).

    Google Scholar 

  15. Wielandt, H.: Unzerlegbare, nicht negative Matrizen. Math. Z.52, 642–648 (1950).

    Google Scholar 

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Heap, B.R., Lynn, M.S. The index of primitivity of a non-negative matrix. Numer. Math. 6, 120–141 (1964). https://doi.org/10.1007/BF01386062

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