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On selfadjoint matrix polynomials

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Abstract

A spectral theory for selfadjoint matrix polynomials is developed. The new concept of a "sign characteristic" is introduced which admits a description of the main spectral properties of such polynomials. Two independent descriptions of the sign characteristic are given. Results concerning an inverse problem, and polynomials nonnegative on the real line are described.

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References

  1. Gohberg, I., Lancaster, P. and Rodman, L.: Spectral Analysis of matrix polynomials, I. Canonical forms and divisors, II. The resolvent form and spectral divisors. Lin. Alg. and Appl. 20 (1978), 1–44; 21 (1978), 65–88.

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Authors and Affiliations

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

    I. Gohberg

  2. Department of Mathematics and Statistics, Univeristy of Calgary, T2N 1N4, Calgary, Canada

    P. Lancaster & L. Rodman

Authors
  1. I. Gohberg
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  2. P. Lancaster
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  3. L. Rodman
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Gohberg, I., Lancaster, P. & Rodman, L. On selfadjoint matrix polynomials. Integr equ oper theory 2, 434–439 (1979). https://doi.org/10.1007/BF01682679

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  • DOI: https://doi.org/10.1007/BF01682679

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