发表机构
Universidad Politécnica de Madrid（马德里理工大学）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
本文针对具有任意谱的无迹实对称矩阵的等谱流形，构造可对角化非周期Toda向量场的坐标，依托新矩阵分解完成该构造，所得坐标的并集覆盖等谱流形，且每组坐标定义域稠密。
AI 中文摘要
我们在具有任意谱的无迹实对称矩阵的正交共轭类（即等谱流形）上构造坐标，这些坐标可对角化非周期Toda向量场。这些坐标定义在任意对角矩阵的邻域上，能将Toda向量场解耦为多个实数域中欧拉向量场的倍数之和。每组坐标的定义域是稠密的，其并集覆盖整个等谱流形。该构造依赖于一个具有独立研究价值的新矩阵分解。
英文摘要
We construct coordinates on orthogonal conjugacy classes of traceless real symmetric matrices with arbitrary spectrum (the isospectral manifold) that diagonalize the non-periodic Toda vector field. The coordinates, defined on a neighborhood of any diagonal matrix decouple the Toda vector field into a sum of multiples of the Euler vector field in $\mathbb{R}$. The domain of each set of coordinates is dense and their union covers the isospectral manifold. The construction relies on a new matrix factorization which is of independent interest.
CommentsSection 3.2 expanded
