Files and links (1)
SubmittedarXiv.org - Non-exclusive license to distribute, Open
Journal article
Stable Noncommutative Polynomials and Their Determinantal Representations
SIAM journal on applied algebra and geometry, v 3(1), 152
01 Jan 2019
Abstract
A noncommutative polynomial is stable if it is nonsingular on all tuples of matrices whose imaginary parts are positive definite. In this paper a characterization of stable polynomials is given in terms of purely stable linear matrix pencils, i.e., pencils of the form H vertical bar iP(0) vertical bar P(1)x(1) vertical bar ... vertical bar P(d)x(d), where H is hermitian and P-j are positive semidefinite matrices. Namely, a noncommutative polynomial is stable if and only if it admits a determinantal representation with a purely stable pencil. More generally, structure certificates for noncommutative stability are given for linear matrix pencils and noncommutative rational functions.
Metrics
Details
- Title
- Stable Noncommutative Polynomials and Their Determinantal Representations
- Creators
- Jurij Volcic - Texas A&M Univ, Dept Math, College Stn, TX 77840 USA
- Publication Details
- SIAM journal on applied algebra and geometry, v 3(1), 152
- Publisher
- Siam Publications
- Number of pages
- 20
- Grant note
- SCHW 1723/1-1 / Deutsche Forschungsgemeinschaft (DFG); German Research Foundation (DFG)
- Resource Type
- Journal article
- Language
- English
- Academic Unit
- Mathematics
- Web of Science ID
- WOS:000462647900008
- Scopus ID
- 2-s2.0-85087046438
- Other Identifier
- 991021861670604721
InCites Highlights
Data related to this publication, from InCites Benchmarking & Analytics tool:
- Web of Science research areas
- Mathematics, Applied