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

A form p on R^n (homogeneous n-variate polynomial) is called positive semidefinite (psd) if it is nonnegative on R^n. In other words, the zero vector is a global minimizer of p in this case. The famous 17th conjecture of Hilbert (later proven by Artin) is that a form p is psd if and only if … Read more