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Stable factorizations of monic matrix polynomials and stable invariant subspaces

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Abstract

The stable factorizations of a monic matrix polynomial are characterized in terms of spectral properties. Proofs are based on the divisibility theory developed by I. Gohberg, P. Lancaster and L. Rodman. A large part of the paper is devoted to a detailed analysis of stable invariant subspaces of a matrix. The results are also used to describe all stable solutions of the operator Riccati equation.

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Authors and Affiliations

  1. Viskundig Seminarium, Vrje Universiteit, 1007 MC, Amsterdam, The Netherlands

    H. Bart & M. A. Kaashoek

  2. Department of Mathematics, Tel-Aviv University, Ramat-Aviv, Israel

    I. Gohberg

Authors
  1. H. Bart
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  2. I. Gohberg
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  3. M. A. Kaashoek
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Bart, H., Gohberg, I. & Kaashoek, M.A. Stable factorizations of monic matrix polynomials and stable invariant subspaces. Integr equ oper theory 1, 496–517 (1978). https://doi.org/10.1007/BF01682938

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  • DOI: https://doi.org/10.1007/BF01682938

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