矩阵切片-spectral theory场景
Slices of matrices - a scenario for spectral theory
摘要：
给定一个实的对称矩阵S，我们定义通过S的切片为两个共轭轨道的包含S的连通分量：第一个由正交群，第二个由上三角群。我们描述了特征值计算和保持切片不变的可积系统中的一些经典结构--它们的性质由这个概念阐明。我们还参数化的封闭切片的凸多胞体。
英文摘要：
Given a real, symmetric matrix S, we define the slice through S as being the connected component containing S of two orbits under conjugation: the first by the orthogonal group, and the second by the upper triangular group. We describe some classical constructions in eigenvalue computations and integrable systems which keep slices invariant -- their properties are clarified by the concept. We also parametrize the closure of a slice in terms of a convex polytope.
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