Linearization of bivariate polynomial matrices expressed in non monomial basis

  • Aikaterini S. Karetsou
  • Nicholas P. Karampetakis


The paper proposes a two step algorithm that reduces a bivariate polynomial matrix \(T\left( s,z\right) \) expressed in Newton or Lagrange base to a bivariate matrix pencil \(A+E_{1}s+E_{2}z\) with the same invariant polynomials and zero structure.


Bivariate polynomial matrix Matrix pencil Companion form Unimodular equivalence Zero coprime equivalence Newton basis Lagrange basis 

Mathematics Subject Classification

Primary: 93B18 Secondary: 93B17 93B25 93B11 93B40 93C05 93C35 



This research has been co-financed by the European Union (European Social Fund ESF) and Greek national funds through the Operational Program “Education and Lifelong Learning” of the National Strategic Reference Framework (NSRF)—Research Funding Program: ARCHIMEDES III. Investing in knowledge society through the European Social Fund.


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Copyright information

© Springer Science+Business Media New York 2014

Authors and Affiliations

  • Aikaterini S. Karetsou
    • 1
  • Nicholas P. Karampetakis
    • 1
  1. 1.Department of MathematicsAristotle University of ThessalonikiThessalonikiGreece

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