谱线性矩阵不等式
Spectral linear matrix inequalities
摘要：
在一定的表示论假设下，证明了特征值满足线性矩阵不等式的实对称矩阵的集合是一个谱面体。主要应用是半正定锥的导数松弛是谱面体。从这一点，我们进一步推导出他们的朗斯基的陈述。这意味着牛顿不等式，以及双曲多项式的相关不等式的加强，可以表示为平方和。
英文摘要：
We prove, under a certain representation theoretic assumption, that the set of real symmetric matrices, whose eigenvalues satisfy a linear matrix inequality, is itself a spectrahedron. The main application is that derivative relaxations of the positive semidefinite cone are spectrahedra. From this we further deduce statements on their Wronskians. These imply that Newton's inequalities, as well as a strengthening of the correlation inequalities for hyperbolic polynomials, can be expressed as sums of squares.
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