Journal article
FACTORIZATION OF SINGULAR MATRIX POLYNOMIALS AND MATRICES WITH CIRCULAR HIGHER RANK NUMERICAL RANGES
SIAM JOURNAL ON MATRIX ANALYSIS AND APPLICATIONS, v 43(3), p1423
2022
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.
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Details
- Title
- FACTORIZATION OF SINGULAR MATRIX POLYNOMIALS AND MATRICES WITH CIRCULAR HIGHER RANK NUMERICAL RANGES
- Publication Details
- SIAM JOURNAL ON MATRIX ANALYSIS AND APPLICATIONS, v 43(3), p1423
- Publisher
- SIAM PUBLICATIONS; PHILADELPHIA
- Grant note
- The work of the second author was partially supported by Faculty Research funding from the Division of Science and Mathematics, New York University Abu Dhabi. The work of the third author was supported by the Simons Foundation grant 355645 and the National Science Foundation grant DMS-2000037.
- Resource Type
- Journal article
- Language
- English
- Academic Unit
- Drexel University
- Web of Science ID
- WOS:001125796400001
- Scopus ID
- 2-s2.0-85138486359
- Other Identifier
- 991021860728604721
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- Collaboration types
- Domestic collaboration
- International collaboration
- Web of Science research areas
- Mathematics, Applied