Abstract
Pairs of linear transformations on a finite dimensional vector space are of great relevance in the analysis of two-dimensional (2D) systems evolutions. In this paper, special properties of matrix pairs, such as finite memory, separability, property L and property P, as well as their dynamical interpretations, are investigated. Practical criteria for testing property L and property P in a finite number of steps are also presented.
The nonnegativity requirement on a matrix pair allows for much stronger characterizations of finite memory and separability, which in fact prove to be structural properties. Finally, the irreducibility and primitivity notions of positive matrix pairs are discussed, and connected with the dynamical behavior of the associated 2D systems.
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Fornasini, E., Marchesini, G., Valcher, M.E. (1997). Matrix Pairs and 2D Systems Analysis. In: Helmke, U., Prätzel-Wolters, D., Zerz, E. (eds) Operators, Systems and Linear Algebra. European Consortium for Mathematics in Industry. Vieweg+Teubner Verlag, Wiesbaden. https://doi.org/10.1007/978-3-663-09823-2_6
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DOI: https://doi.org/10.1007/978-3-663-09823-2_6
Publisher Name: Vieweg+Teubner Verlag, Wiesbaden
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