The structure of nonsingular polynomial matrices |
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Authors: | Harald K Wimmer |
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Affiliation: | 1. Mathematisches Institut, Universit?t Würzburg, D-8700, Würzburg, West Germany
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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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