Directed graphs, 2D state models, and characteristic polynomials of irreducible matrix pairs

Linear Algebra and Its Applications

Volumn 263, Issue 1-3, 1997, Pages 275-310

  Fornasini, Ettore ^a   Valcher, Maria Elena ^a  

^a UNIVERSITY OF PADOVA   (Italy)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 0040689406     PISSN: 00243795     EISSN: None     Source Type: Journal    
DOI: 10.1016/S0024-3795(96)00540-X     Document Type: Article

References (11)

1. A. Berman and R. J. Plemmons, Nonnegative Matrices in the Mathematical Sciences, Academic, New York, 1979.
2. N. K. Bose, Multidimensional Systems Theory, Reidel, Dordrecht, 1985.
3. R. A. Brualdi and H. J. Ryser, Combinatorial Matrix Theory, Cambridge U.P., Cambridge, 1991.
4. J. W. Cassels, An Introduction to the Geometry of Numbers, Springer-Verlag, Berlin, 1959.
5. E. Fornasini and G. Marchesini, Doubly indexed dynamical systems, Math. Systems Theory 12:59-72 (1978).
6. E. Fornasini and G. Marchesini, Properties of pairs of matrices and state-models for 2D systems, in Multivariate Analysis: Future Directions, Vol. 5 (C. R. Rao, Ed.), North-Holland Ser. Probab. and Statist., 1993, pp. 131-180.
7. E. Fornasini and M. E. Valcher, Matrix pairs in 2D systems: An approach based on trace series and Hankel matrices, SIAM J. Control Optim. 33(4):1127-1150 (1995).
8. E. Fornasini and M. E. Valcher, Primitivity of positive matrix pairs: algebraic Characterization, graph-theoretic description and 2D systems interpretation, Siam. J. Matrix Analysis and Appl., to appear.
9. G. H. Hardy and E. M. Wright, An Introduction to the Theory of Numbers, Oxford Science, 1979.
10. J. G. Kemeny and J. L. Snell, Finite Markov Chains, Van Nostrand Reinhold, New York, 1960.
11. H. Minc, Nonnegative Matrices, Wiley, New York, 1988.