Positive polynomials and hyperdeterminants

Let F be a homogeneous real polynomial of even degree in any number of variables. We consider the problem of giving explicit conditions on the coefficients so that F is positive definite or positive semi-definite. In this note we produce a necessary condition for positivity, and a sufficient conditi...

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Detalles Bibliográficos
Autor principal: Cukierman, Fernando
Publicado: 2007
Materias:
Characteristic polynomial
Discriminant
Hyperdeterminant
Positive
Acceso en línea:https://bibliotecadigital.exactas.uba.ar/collection/paper/document/paper_00100757_v58_n3_p279_Cukierman
http://hdl.handle.net/20.500.12110/paper_00100757_v58_n3_p279_Cukierman
Aporte de:
Biblioteca Digital - Facultad de Ciencias Exactas y Naturales (UBA) de Universidad de Buenos Aires
id paper:paper_00100757_v58_n3_p279_Cukierman
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spelling paper:paper_00100757_v58_n3_p279_Cukierman2023-06-08T14:34:16Z Positive polynomials and hyperdeterminants Cukierman, Fernando Characteristic polynomial Discriminant Hyperdeterminant Positive Let F be a homogeneous real polynomial of even degree in any number of variables. We consider the problem of giving explicit conditions on the coefficients so that F is positive definite or positive semi-definite. In this note we produce a necessary condition for positivity, and a sufficient condition for non-negativity, in terms of positivity or semi-positivity of a one-variable characteristic polynomial of F. Also, we revisit the known sufficient condition in terms of Hankel matrices. © 2007 Universität de Barcelona. Fil:Cukierman, F. Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales; Argentina. 2007 https://bibliotecadigital.exactas.uba.ar/collection/paper/document/paper_00100757_v58_n3_p279_Cukierman http://hdl.handle.net/20.500.12110/paper_00100757_v58_n3_p279_Cukierman
institution Universidad de Buenos Aires
institution_str I-28
repository_str R-134
collection Biblioteca Digital - Facultad de Ciencias Exactas y Naturales (UBA)
topic Characteristic polynomial
Discriminant
Hyperdeterminant
Positive
spellingShingle Characteristic polynomial
Discriminant
Hyperdeterminant
Positive
Cukierman, Fernando
Positive polynomials and hyperdeterminants
topic_facet Characteristic polynomial
Discriminant
Hyperdeterminant
Positive
description Let F be a homogeneous real polynomial of even degree in any number of variables. We consider the problem of giving explicit conditions on the coefficients so that F is positive definite or positive semi-definite. In this note we produce a necessary condition for positivity, and a sufficient condition for non-negativity, in terms of positivity or semi-positivity of a one-variable characteristic polynomial of F. Also, we revisit the known sufficient condition in terms of Hankel matrices. © 2007 Universität de Barcelona.
author Cukierman, Fernando
author_facet Cukierman, Fernando
author_sort Cukierman, Fernando
title Positive polynomials and hyperdeterminants
title_short Positive polynomials and hyperdeterminants
title_full Positive polynomials and hyperdeterminants
title_fullStr Positive polynomials and hyperdeterminants
title_full_unstemmed Positive polynomials and hyperdeterminants
title_sort positive polynomials and hyperdeterminants
publishDate 2007
url https://bibliotecadigital.exactas.uba.ar/collection/paper/document/paper_00100757_v58_n3_p279_Cukierman
http://hdl.handle.net/20.500.12110/paper_00100757_v58_n3_p279_Cukierman
work_keys_str_mv AT cukiermanfernando positivepolynomialsandhyperdeterminants
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