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Hyperbolicity cones of elementary symmetric polynomials are spectrahedral

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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.

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Authors and Affiliations

  1. Department of Mathematics, Royal Institute of Technology, 100 44 , Stockholm, Sweden

    Petter Brändén

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  1. Petter Brändén
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Correspondence to Petter Brändén.

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PB is a Royal Swedish Academy of Sciences Research Fellow supported by a grant from the Knut and Alice Wallenberg Foundation. The research is also supported by the Göran Gustafsson Foundation.

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Brändén, P. Hyperbolicity cones of elementary symmetric polynomials are spectrahedral. Optim Lett 8, 1773–1782 (2014). https://doi.org/10.1007/s11590-013-0694-6

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