Mathematical systems theory

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

The structure of nonsingular polynomial matrices

  • Harald K. Wimmer


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.


Computational Mathematic Shift Operator Elementary Divisor Generalize Eigenvector Polynomial Matrice 
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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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