Journal article
Positive univariate trace polynomials
Journal of algebra, v 579, pp 303-317
01 Aug 2021
Abstract
A univariate trace polynomial is a polynomial in a variable x and formal trace symbols Tr(xj). Such an expression can be naturally evaluated on matrices, where the trace symbols are evaluated as normalized traces. This paper addresses global and constrained positivity of univariate trace polynomials on symmetric matrices of all finite sizes. A tracial analog of Artin's solution to Hilbert's 17th problem is given: a positive semidefinite univariate trace polynomial is a quotient of sums of products of squares and traces of squares of trace polynomials.
Metrics
Details
- Title
- Positive univariate trace polynomials
- Creators
- Igor Klep - University of LjubljanaJames Eldred Pascoe - University of FloridaJurij Volčič - Texas A&M University
- Publication Details
- Journal of algebra, v 579, pp 303-317
- Publisher
- Elsevier
- Grant note
- J1-2453; P1-0222 / Slovenian Research Agency (https://doi.org/10.13039/501100004329) DMS-1954709 / NSF (https://doi.org/10.13039/100000001) DMS-1953963; DMS-1606260 / NSF (https://doi.org/10.13039/100000001)
- Resource Type
- Journal article
- Language
- English
- Academic Unit
- Mathematics
- Web of Science ID
- WOS:000642101400014
- Scopus ID
- 2-s2.0-85103698124
- Other Identifier
- 991021879625304721
InCites Highlights
Data related to this publication, from InCites Benchmarking & Analytics tool:
- Collaboration types
- Domestic collaboration
- International collaboration
- Web of Science research areas
- Mathematics