Dimension of gram spectrahedra of univariate polynomials

TL;DR

This paper determines the dimension of Gram Spectrahedra for univariate polynomials, providing insights into their geometric structure and the space of sums-of-squares representations.

Contribution

It introduces a precise calculation of the dimension of Gram Spectrahedra specifically for univariate polynomials, advancing understanding of their geometric properties.

Findings

Dimension formulas for Gram Spectrahedra of univariate polynomials

Enhanced understanding of sums-of-squares representations

Geometric characterization of Gram Spectrahedra

Abstract

The Gram Spectrahedron of a polynomial parametrizes its sums-of-squares representations. In this note, we determine the dimension of Gram Spectrahedra of univariate polynomials.