Directed graphs, 2D state models, and characteristic polynomials of irreducible matrix pairs. (English) Zbl 0887.93033
A notion of a 2D digraph and a 2D strongly connected digraph are introduced. Equivalent descriptions of the irreducibility of matrices are obtained. Dynamical characterizations of irreducible matrix pairs and their characteristic polynomials are presented. Primitivity is introduced as a special case of irreducibility of matrix pairs.
Reviewer: T.Kaczorek (Warszawa)
MSC:
| 93C35 | Multivariable systems, multidimensional control systems |
| 05C38 | Paths and cycles |
| 05C40 | Connectivity |
| 05C50 | Graphs and linear algebra (matrices, eigenvalues, etc.) |
| 05C75 | Structural characterization of families of graphs |
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