Primes in several classes of the positive matrices

Linear Algebra and Its Applications

Volumn 277, Issue 1-3, 1998, Pages 149-185

  Picci, G ^a   Van Den Hof, J M ^b   Van Schuppen, J H ^b  

^a UNIVERSITY OF PADOVA   (Italy)

^b CWI   (Netherlands)

Author keywords

Doubly stochastic circulant; Doubly stochastic matrix; Positive matrix; Prime

Indexed keywords

EID: 0041876712     PISSN: 00243795     EISSN: None     Source Type: Journal    
DOI: 10.1016/S0024-3795(97)10060-X     Document Type: Article

References (22)

1. A. Berman, M. Neumann, R.J. Stern, Nonnegative Matrices in Dynamic Systems, Wiley, New York, 1989.
2. A. Berman, R.J. Plemmons, Nonnegative Matrices in the Mathematical Sciences, Academic Press, New York, 1979.
3. A. Berman, R.J. Plemmons, Nonnegative matrices in the mathematical sciences, Number 9 in Classics in Applied Mathematics, SIAM, Philadelphia, 1993.
4. R.A. Brualdi, S.V. Parter, H. Schneider, The diagonal equivalence of a nonnegative matrix to a stochastic matrix, J. Math. Anal. Appl. 16 (1966) 31-50.
5. R.A. Brualdi, H.J. Ryser, Combinatorial Matrix Theory, Cambridge University Press, Cambridge, 1991.
6. P.J. Davis, Circulant Matrices, Wiley, New York, 1979.
7. D. de Caen, D.A. Gregory, Primes in the semigroup of boolean matrices, Linear Algebra Appl. 37 (1981) 119-134.
8. J. Dénes, A.D. Keedwell, Latin Squares: New Developments in the Theory and Applications, North-Holland, Amsterdam, 1991.
9. J. Dieudonné, Foundations of Modern Analysis, Academic Press, New York, 1969.
10. F.R. Gantmacher, The Theory of Matrices, vols. 1/2, Chelsea, New York, 1959.
11. J.S. Golan, The Theory of Semirings with Applications in Mathematics and Theoretical Computer Science, Longman, Harlow, 1992.
12. N. Jacobson, Basic Algebra, vols. 1/2, 2nd edn., Freeman, New York, 1985.
13. M. Lewin, On nonnegative matrices, Pacific J. Math. 36 (1971) 753-759.
14. D. London, On matrices with a doubly stochastic pattern, J. Math. Anal. Appl. 34 (1971) 648-652.
15. M. Marcus, K. Kidman, M. Sandy, Products of elementary doubly stochastic matrices, Linear and Multilinear Algebra 15 (1984) 331-340.
16. A.W. Marshall, I. Olkin, Inequalities: Theory of Majorization and its Applications, Academic Press, New York, 1979.
17. H. Mine, Nonnegative Matrices, Wiley, New York, 1988.
18. L. Mirsky, Results and problems in the theory of doubly stochastic matrices, Z. Wahrscheinlichkeitstheorie 1 (1963) 319-334.
19. B.N. Parlett, T.L. Landis, Methods for scaling to doubly stochastic form, Linear Algebra Appl. 48 (1982) 53-79.
20. H. Perfect, L. Mirsky, The distribution of positive elements in doubly stochastic matrices, J. London Math. Soc. 40 (1965) 689-698.
21. G. Picci, J.H. van Schuppen, Stochastic realization of finite-valued processes and primes in the positive matrices, in: H. Kimura, S. Kodama (Eds.), Recent advances in mathematical theory of systems, control, networks, and signal processing II, Proceedings of the International Symposium MTNS-91, Mita Press, Tokyo, 1992, pp. 227-232.
22. D.J. Richman, H. Schneider, Primes in the semigroup of non-negative matrices, Linear and Multilinear Algebra 2 (1974) 135-140.