Products of positive forms, linear matrix inequalities, and Hilbert 17th problem for ternary forms

• Main Authors: Klerk, Etienne de., Pasechnik, Dmitrii V.
• Other Authors: School of Physical and Mathematical Sciences
• Format: Article
• Language: English
• Published: 2012
• Subjects: DRNTU::Science::Mathematics::Discrete mathematics::Theory of computation
• Online Access: https://hdl.handle.net/10356/95694; http://hdl.handle.net/10220/8271
• Institution: Nanyang Technological University

A form p on Rn (homogeneous n-variate polynomial) is called positive semidefinite (p.s.d.) if it is nonnegative on Rn. In other words, the zero vector is a global minimizer of p in this case. The famous 17th conjecture of Hilbert [Bull. Amer. Math. Soc. (N.S.), 37 (4) (2000) 407] (later proven by Ar...