Journal article
Indefinite determinantal representations versus nonsingularities on the noncommutative d-torus
Linear algebra and its applications, v 720, pp 245-255
01 Sep 2025
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Abstract
We show that for a multivariable polynomial
with a determinantal representation
the matrix K is structurally similar to a strictly J-contractive matrix for some diagonal signature matrix J if and only if the extension of
to a polynomial in d-tuples of matrices of arbitrary size given by
where
,
, does not have roots on the noncommutative d-torus consisting of d-tuples
of unitary matrices of arbitrary size.
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Details
- Title
- Indefinite determinantal representations versus nonsingularities on the noncommutative d-torus
- Creators
- Gilbert J. Groenewald - North-West UniversitySanne ter HorstHugo J. Woerdeman - Drexel University
- Publication Details
- Linear algebra and its applications, v 720, pp 245-255
- Publisher
- Elsevier
- Number of pages
- 11
- Grant note
- National Research Foundation of South Africa (NRF): 118513, 127364 DSI-NRF Centre of Excellence in Mathematical and Statistical Sciences (CoE-MaSS)National Graduate Academy for Mathematical and Statistical Sciences (NGA(MaSS))University Capacity Development Programme (UCDP) from the Department of Higher Education and Training (DHET)United States National Science Foundation (NSF): DMS-2000037, DMS-2348720
This work is based on research supported in part by the National Research Foundation of South Africa (NRF, Grant Numbers 118513 and 127364) and the DSI-NRF Centre of Excellence in Mathematical and Statistical Sciences (CoE-MaSS). Any opinion, finding and conclusion or recommendation expressed in this material is that of the authors and the NRF and CoE-MaSS do not accept any liability in this regard. We also gratefully acknowledge funding from the National Graduate Academy for Mathematical and Statistical Sciences (NGA(MaSS)) and the University Capacity Development Programme (UCDP) from the Department of Higher Education and Training (DHET). In addition, HW is partially supported by United States National Science Foundation (NSF) grants DMS-2000037 and DMS-2348720.
- Resource Type
- Journal article
- Language
- English
- Academic Unit
- Mathematics
- Web of Science ID
- WOS:001491763900005
- Scopus ID
- 2-s2.0-105004660767
- Other Identifier
- 991022052806004721
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- Collaboration types
- Domestic collaboration
- International collaboration
- Web of Science research areas
- Mathematics
- Mathematics, Applied