论文标题
光谱多面体
Spectral Polyhedra
论文作者
论文摘要
“光谱凸组集”是对称矩阵的集合，其特征值范围形成对称凸组。频谱凸点概括了Sanyal-Sottile-Sturmfels（2011）研究的Schur-Horn轨道。我们研究了这类凸体，该体是在交叉点，极性和Minkowski总和下关闭的。我们描述了面部轨道，并为其施泰纳多项式提供了一个公式。然后，我们专注于光谱多面体。我们证明频谱Polyhedra是光谱，并给出少量表示作为光谱的阴影。我们关闭有关双曲线锥，极性凸体和光谱分子型的观察和问题。
A "spectral convex set" is a collection of symmetric matrices whose range of eigenvalues form a symmetric convex set. Spectral convex sets generalize the Schur-Horn orbitopes studied by Sanyal-Sottile-Sturmfels (2011). We study this class of convex bodies, which is closed under intersections, polarity, and Minkowski sums. We describe orbits of faces and give a formula for their Steiner polynomials. We then focus on spectral polyhedra. We prove that spectral polyhedra are spectrahedra and give small representations as spectrahedral shadows. We close with observations and questions regarding hyperbolicity cones, polar convex bodies, and spectral zonotopes.
