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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todo:paper_00100757_v58_n3_p279_Cukierman2023-10-03T14:08:58Z Positive polynomials and hyperdeterminants Cukierman, F. 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. JOUR info:eu-repo/semantics/openAccess http://creativecommons.org/licenses/by/2.5/ar 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 |
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Biblioteca Digital - Facultad de Ciencias Exactas y Naturales (UBA) |
topic |
Characteristic polynomial Discriminant Hyperdeterminant Positive |
spellingShingle |
Characteristic polynomial Discriminant Hyperdeterminant Positive Cukierman, F. 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. |
format |
JOUR |
author |
Cukierman, F. |
author_facet |
Cukierman, F. |
author_sort |
Cukierman, F. |
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 |
url |
http://hdl.handle.net/20.500.12110/paper_00100757_v58_n3_p279_Cukierman |
work_keys_str_mv |
AT cukiermanf positivepolynomialsandhyperdeterminants |
_version_ |
1807324168886157312 |