Hyperbolicity cones of elementary symmetric polynomials are spectrahedral

Abstract

We prove that the hyperbolicity cones of elementary symmetric polynomials are spectrahedral, i.e., they are slices of the cone of positive semidefinite matrices. The proof uses the matrix--tree theorem, an idea already present in Choe et al.

9 pages. Some typos corrected. Details added. To appear in Optimization Letters

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