Supplementary Information 5 Dynamical Similarity We consider the problem of determining when two linear autonomous dynamical systems on R n x = Ax and y = By (9)

Unfortunately, this measure of similarity requires solving a nonconvex optimization problem. All elements of O (n) /SO ( n) are bijective maps between itself and SO (n) . Then we can show by the same logic that PD O (n) /SO ( n). According to Williams et al. [2021], only two things are needed. Then we must show that the similarity transform is an isometry: g (T (A), T(B)) = g ( A, B) (17) where T ( A) is a map that in our case is the similarity transform. Here we demonstrate how V ector Fields transform.