Smoothness properties of principal angles between subspaces with applications to angular values of dynamical systems
Dynamical Systems
2024-04-04 v2
Abstract
In this work we provide detailed estimates of maximal principal angles between subspaces and we analyze their smoothness for smoothly varying subspaces. This leads to a new definition of angular values for linear dynamical systems in continuous time. We derive some of their properties complementary to the theory of angular values developed in [W.-J. Beyn, G. Froyland, and T. H\"uls, SIAM J. Appl. Dyn. Syst., 21 (2022), pp. 1245--1286], [W.-J. Beyn, and T. H\"uls, SIAM J. Appl. Dyn. Syst., 22 (2023), pp. 162--198] for discrete time systems. The estimates are further employed to establish upper semicontinuity of angular values for some parametric model examples of discrete and continuous type.
Cite
@article{arxiv.2303.07918,
title = {Smoothness properties of principal angles between subspaces with applications to angular values of dynamical systems},
author = {Wolf-Jürgen Beyn and Thorsten Hüls},
journal= {arXiv preprint arXiv:2303.07918},
year = {2024}
}