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arXiv · 2303.07918

Smoothness properties of principal angles between subspaces with applications to angular values of dynamical systems

Wolf-Jürgen Beyn·Thorsten Hüls
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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.

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Wolf-Jürgen Beyn, Thorsten Hüls. 2023-03-14. Smoothness properties of principal angles between subspaces with applications to angular values of dynamical systems. https://doi.org/10.1080/14689367.2024.2322156

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