Real symmetric matrices with partitioned eigenvalues

被引：0
|
作者：
Weinstein, Madeleine
机构：
来源：
LINEAR ALGEBRA AND ITS APPLICATIONS | 2022年 / 633卷
基金：
美国国家科学基金会;
关键词：
Real algebraic variety; Real symmetric matrices; Euclidean distance degree; Degenerate matrices; DISCRIMINANT;
D O I：
10.1016/j.laa.2021.10.016
中图分类号：
O29 [应用数学];
学科分类号：
070104 ;
摘要：
We study the real algebraic variety of real symmetric matrices with eigenvalue multiplicities determined by a partition. We present formulas for the dimension and Euclidean distance degree. We give a parametrization by rational functions. For small matrices, we provide equations; for larger matrices, we explain how to use representation theory to find equations. We describe the ring of invariants under the action of the orthogonal group. For the subvariety of diagonal matrices, we give the degree. (C) 2021 Elsevier Inc. All rights reserved.
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页码：281 / 289
页数：9
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