A Linear-algebraic Proof of Hilbert's Ternary Quartic Theorem
Algebraic Geometry
2019-05-14 v1
Abstract
Hilbert's ternary quartic theorem states that every nonnegative degree 4 homogeneous polynomial in three variables can be written as a sum of three squares of homogeneous quadratic polynomials. We give a linear-algebraic approach to Hilbert's theorem by showing that a structured cone of positive semidefinite matrices is generated by rank 1 elements.
Cite
@article{arxiv.1905.04751,
title = {A Linear-algebraic Proof of Hilbert's Ternary Quartic Theorem},
author = {Anatolii Grinshpan and Hugo J. Woerdeman},
journal= {arXiv preprint arXiv:1905.04751},
year = {2019}
}