A permuted factors approach for the linearization of polynomial matrices |
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Authors: | S Vologiannidis E N Antoniou |
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Affiliation: | 1. Department of Mathematics, Aristotle University of Thessaloniki, 54006, Thessaloniki, Greece 2. Department of Sciences, Technological Educational Institute of Thessaloniki, 57400, Sindos, Greece
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Abstract: | In Antoniou and Vologiannidis (Electron J Linear Algebra 11:78–87, 2004; 15:107–114, 2006), a new family of companion forms associated with a regular polynomial matrix T (s) has been presented, using products of permutations of n elementary matrices, generalizing similar results presented in Fiedler (Linear Algebra Its Appl 371:325–331, 2003) where the scalar case was considered. In this paper, extending this “permuted factors” approach, we present a broader family
of companion-like linearizations, using products of up to n(n−1)/2 elementary matrices, where n is the degree of the polynomial matrix. Under given conditions, the proposed linearizations can be shown to consist of block
entries where the coefficients of the polynomial matrix appear intact. Additionally, we provide a criterion for those linearizations
to be block symmetric. We also illustrate several new block symmetric linearizations of the original polynomial matrix T (s), where in some of them the constraint of nonsingularity of the constant term and the coefficient of maximum degree are not
a prerequisite. |
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