FACTORIZATION OF SINGULAR MATRIX POLYNOMIALS AND MATRICES WITH CIRCULAR HIGHER RANK NUMERICAL RANGES

Edward Poon, Ilya M. Spitkovsky, Hugo J. Woerdeman

Research output: Contribution to journalArticlepeer-review

Abstract

Factorization of regular Hermitian valued trigonometric polynomials (on the unit circle) and Hermitian valued polynomials (on the real line) have been studied well. In this paper we drop the condition of regularity and study factorization of singular Hermitian valued (trigonometric) polynomials. We subsequently apply the results to obtain a characterization of matrices with a circular higher rank numerical range and derive a new version of Anderson's theorem. As a special case, we obtain a new characterization of matrices with a circular numerical range.

Original languageEnglish (US)
Pages (from-to)1423-1439
Number of pages17
JournalSIAM Journal on Matrix Analysis and Applications
Volume43
Issue number3
DOIs
StatePublished - 2022

Keywords

  • circular numerical range
  • Hermitian valued trigonometric polynomials
  • higher rank numerical range
  • J-spectral factorization

ASJC Scopus subject areas

  • Analysis

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