# Positive polynomials and hyperdeterminants

Collectanea Mathematica (2007)

- Volume: 58, Issue: 3, page 279-289
- ISSN: 0010-0757

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topCukierman, 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 -

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