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.
@article{urn:eudml:doc:42037,
title = {Positive polynomials and hyperdeterminants},
journal = {Collectanea Mathematica},
volume = {58},
year = {2007},
pages = {279-289},
zbl = {1134.13020},
language = {en},
url = {http://dml.mathdoc.fr/item/urn:eudml:doc:42037}
}
Cukierman, Fernando. Positive polynomials and hyperdeterminants. Collectanea Mathematica, Tome 58 (2007) pp. 279-289. http://gdmltest.u-ga.fr/item/urn:eudml:doc:42037/