  A popular way to approximate the Koopman operator's action on a
finite-dimensional subspace of functions is via orthogonal projections. The
quality of the projected model directly depends on the selected subspace,
specifically on how close it is to being invariant under the Koopman operator.
The notion of invariance proximity provides a tight upper bound on the
worst-case relative prediction error of the finite-dimensional model. However,
its direct calculation is computationally challenging. This paper leverages the
geometric structure behind the definition of invariance proximity to provide a
closed-form expression in terms of Jordan principal angles on general inner
product spaces. Unveiling this connection allows us to exploit specific
isomorphisms to circumvent the computational challenges associated with spaces
of functions and enables the use of existing efficient numerical routines to
compute invariance proximity.
