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Mathematical systems theory

, Volume 14, Issue 1, pp 367–379 | Cite as

The structure of nonsingular polynomial matrices

  • Harald K. Wimmer
Article

Abstract

LetK be a field and letL ∈ Kn × n [z] be nonsingular. The matrixL can be decomposed as\(L(z) = \hat Q(z)(Rz + S)\hat P(z)\) so that the finite and (suitably defined) infinite elementary divisors ofL are the same as those ofRz + S, and\(\hat Q(z)\) and\(\hat P(z)^T\) are polynomial matrices which have a constant right inverse. If
$$Rz + S = \left( {\begin{array}{*{20}c} {zI - A} & 0 \\ 0 & {I - zN} \\ \end{array} } \right)$$
andK is algebraically closed, then the columns of\(\hat Q\) and\(\hat P^T\) consist of eigenvectors and generalized eigenvectors of shift operators associated withL.

Keywords

Computational Mathematic Shift Operator Elementary Divisor Generalize Eigenvector Polynomial Matrice 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Copyright information

© Springer-Verlag New York Inc 1981

Authors and Affiliations

  • Harald K. Wimmer
    • 1
  1. 1.Mathematisches InstitutUniversität WürzburgWürzburgWest Germany

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