Positive polynomials and hyperdeterminants

Cukierman, Fernando. "Positive polynomials and hyperdeterminants." Collectanea Mathematica 58.3 (2007): 279-289. <http://eudml.org/doc/42037>.

@article{Cukierman2007,
abstract = {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.},
author = {Cukierman, Fernando},
journal = {Collectanea Mathematica},
keywords = {positive definite; discriminant; hyperderminant; characteristic polynomial; positive semi-definite; Hankel matrices},
language = {eng},
number = {3},
pages = {279-289},
title = {Positive polynomials and hyperdeterminants},
url = {http://eudml.org/doc/42037},
volume = {58},
year = {2007},
}

TY - JOUR
AU - Cukierman, Fernando
TI - Positive polynomials and hyperdeterminants
JO - Collectanea Mathematica
PY - 2007
VL - 58
IS - 3
SP - 279
EP - 289
AB - 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.
LA - eng
KW - positive definite; discriminant; hyperderminant; characteristic polynomial; positive semi-definite; Hankel matrices
UR - http://eudml.org/doc/42037
ER -