Journal article
The Interplay between Two Kinds of Hermitian Determinantal Representations
SIAM journal on matrix analysis and applications, v 46(2), pp 1346-1377
30 Jun 2025
Abstract
This paper investigates the interplay between two kinds of Hermitian determinantal representations for multivariate polynomials. The first, Hermitian block determinantal representations, have been studied in relation to stability theory. The second, Hermitian additive determinantal representations, have been studied in relation to hyperbolic polynomials and the Lax conjecture. For each kind of Hermitian determinantal representation, we show necessary and sufficient conditions for a multivariate polynomial to have that representation. In particular, this condition requires that a related polynomial have the other type of Hermitian determinantal representation. Thus, if one can characterize when a polynomial has one of these representations, our results will provide a characterization for when a polynomial has the other type of representation.
Metrics
1 Record Views
Details
- Title
- The Interplay between Two Kinds of Hermitian Determinantal Representations
- Creators
- Sarah Gift - Drexel UniversityHugo J. Woerdeman - Drexel University
- Publication Details
- SIAM journal on matrix analysis and applications, v 46(2), pp 1346-1377
- Publisher
- Society for Industrial and Applied Mathematics
- Number of pages
- 32
- Grant note
- National Science Foundation: DMS-2000037
Funding: This work was supported by National Science Foundation grant DMS-2000037.
- Resource Type
- Journal article
- Language
- English
- Academic Unit
- Mathematics
- Web of Science ID
- WOS:001503601900004
- Scopus ID
- 2-s2.0-105006658693
- Other Identifier
- 991022054027604721
InCites Highlights
Data related to this publication, from InCites Benchmarking & Analytics tool:
- Web of Science research areas
- Mathematics, Applied