Article ID | Journal | Published Year | Pages | File Type |
---|---|---|---|---|
4598683 | Linear Algebra and its Applications | 2016 | 7 Pages |
Abstract
A famous theorem of Hilbert from 1888 states that for given n and d, every positive semidefinite (psd) real form of degree 2d in n variables is a sum of squares (sos) of real forms if and only if n=2n=2 or d=1d=1 or (n,2d)=(3,4)(n,2d)=(3,4). In 1976, Choi and Lam proved the analogue of Hilbert's Theorem for symmetric forms by assuming the existence of psd not sos symmetric n -ary quartics for n≥5n≥5. In this paper we complete their proof by constructing explicit psd not sos symmetric n -ary quartics for n≥5n≥5.
Related Topics
Physical Sciences and Engineering
Mathematics
Algebra and Number Theory
Authors
Charu Goel, Salma Kuhlmann, Bruce Reznick,