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IMA Journal of Mathematical Control and Information 1996 13(1):1-11; doi:10.1093/imamci/13.1.1
© 1996 by Institute of Mathematics and its Applications
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Geometric properties, invariants, and the Toeplitz structure of minimal bases of rational vector spaces

NICOS KARCANIAS

Control Engineering Centre, Department of Electrical, Electronic, and Information Engineering, City University Northampton Square, London ECIV 0HB

The algebraic and geometric aspects of a minimal base of a rational vector space {chi} are further developed by exploring the structure of an ordered minimal base (omb) and establishing the properties of its Toeplitz representation. The R(s)-prime modules are introduced as new invariants of {chi}, and each module is characterized by invariant real spaces: the high, low, and prime spaces respectively. Using the Topelitz representation of ombs, the families of primitive and composite spaces are introduced as new invariants of {chi} and their properties are established. The geometric results presented here have implications in the study of the dynamics of polynomial system models and in the computation of minimal bases.


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