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The structure of nonsingular polynomial matrices

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Abstract

LetK be a field and letL ∈ K n × 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.

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  1. Mathematisches Institut, Universität Würzburg, D-8700, Würzburg, West Germany

    Harald K. Wimmer

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  1. Harald K. Wimmer
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Wimmer, H.K. The structure of nonsingular polynomial matrices. Math. Systems Theory 14, 367–379 (1981). https://doi.org/10.1007/BF01752407

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  • DOI: https://doi.org/10.1007/BF01752407

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