论文标题
光谱线性基质不等式
Spectral linear matrix inequalities
论文作者
论文摘要
我们在某些表示理论假设下证明，真实对称矩阵的集合（其特征值满足线性基质不等式）本身就是一种频谱。主要应用是阳性半芬锥的衍生性弛豫是光谱。由此，我们进一步推断出他们的鲁斯克人的陈述。这些暗示牛顿的不平等以及增强双曲线多项式的相关性不平等，也可以表示为正方形之和。
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.
