共轭轨道交点的多面体参数化
Parametrization by polytopes of intersections of orbits by conjugation
摘要：
设S是n × n实对称矩阵，具有谱分解S=Q^T λ Q，其中Q是正交矩阵，λ是具有简单谱{λ 1，.，lambda_n}。又设O_S e R_S为S分别与正交矩阵和具有正对角的上三角形矩阵共轭的轨道。用F_S表示O_S和R_S的交点。证明了从F_S的闭包到R^n，取S' =（Q'）^T λ Q'到diag（Q' λ（Q '）^T）的映射F是到它的值域P_S上的光滑双射，P_S是n的某个子集的凸包！置换（pixeda_1，...，lambda_n）。我们还找到了P_S有n的充要条件！顶点。
英文摘要：
Let S be an nXn real symmetric matrix with spectral decomposition S=Q^T Lambda Q, where Q is an orthogonal matrix and Lambda is diagonal with simple spectrum {lambda_1,..., lambda_n}. Also let O_S e R_S be the orbits by conjugation of S by, respectively, orthogonal matrices and upper triangular matrices with positive diagonal. Denote by F_S the intersection O_S and R_S. We show that the map F tha goes from the closure of F_S to R^n and takes S' = (Q')^T Lambda Q' to diag(Q' Lambda (Q')^T) is a smooth bijection onto its range P_S, the convex hull of some subset of the n! permuatations of (lambda_1, ..., lambda_n). We also find necessary and sufficient conditions for P_S to have n! vertices.
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