Positive univariate trace polynomials

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Standard

Positive univariate trace polynomials. / Klep, I.; Pascoe, J.E.; Volčič, J.

I: Journal of Algebra, Bind 579, 2021, s. 303-317.

Publikation: Bidrag til tidsskrift › Tidsskriftartikel › Forskning › fagfællebedømt

Harvard

Klep, I, Pascoe, JE & Volčič, J 2021, 'Positive univariate trace polynomials', Journal of Algebra, bind 579, s. 303-317. https://doi.org/10.1016/j.jalgebra.2021.03.027

APA

Klep, I., Pascoe, J. E., & Volčič, J. (2021). Positive univariate trace polynomials. Journal of Algebra, 579, 303-317. https://doi.org/10.1016/j.jalgebra.2021.03.027

Vancouver

Klep I, Pascoe JE, Volčič J. Positive univariate trace polynomials. Journal of Algebra. 2021;579:303-317. https://doi.org/10.1016/j.jalgebra.2021.03.027

Author

Klep, I. ; Pascoe, J.E. ; Volčič, J. / Positive univariate trace polynomials. I: Journal of Algebra. 2021 ; Bind 579. s. 303-317.

Bibtex

@article{e5f5e8791e704427bf941491d710566c,
title = "Positive univariate trace polynomials",
abstract = "A univariate trace polynomial is a polynomial in a variable x and formal trace symbols . 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.",
author = "I. Klep and J.E. Pascoe and J. Vol{\v c}i{\v c}",
year = "2021",
doi = "10.1016/j.jalgebra.2021.03.027",
language = "English",
volume = "579",
pages = "303--317",
journal = "Journal of Algebra",
issn = "0021-8693",
publisher = "Academic Press",

}

RIS

TY - JOUR

T1 - Positive univariate trace polynomials

AU - Klep, I.

AU - Pascoe, J.E.

AU - Volčič, J.

PY - 2021

Y1 - 2021

N2 - A univariate trace polynomial is a polynomial in a variable x and formal trace symbols . 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.

AB - A univariate trace polynomial is a polynomial in a variable x and formal trace symbols . 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.

UR - http://www.scopus.com/inward/record.url?eid=2-s2.0-85103698124&partnerID=MN8TOARS

U2 - 10.1016/j.jalgebra.2021.03.027

DO - 10.1016/j.jalgebra.2021.03.027

M3 - Journal article

VL - 579

SP - 303

EP - 317

JO - Journal of Algebra

JF - Journal of Algebra

SN - 0021-8693

ER -

ID: 284012325