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In this work we provide detailed estimates of maximal principal anglesbetween subspaces and we analyze their smoothness for smoothly varyingsubspaces. This leads to a new definition of angular values for lineardynamical systems in continuous time. We derive some of their propertiescomplementary 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 establishupper semicontinuity of angular values for some parametric model examples ofdiscrete and continuous type.

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