The asymptotic behavior of the singular values of matrix powers and applications

The behavior of the singular values Sk(An), k = 1,2,...,r, of the nth power of an r × r matrix A is analyzed for n -> infinity . One of the main results gives for each k an explicit construction of a sequence of the form (a(k)nnl(k)) infinity n=1 which is equivalent to the sequence (Sk(An)) infinity n=1. Analogous results are derived for the continuous case, where An is replaced by exp(tA). Applications concern kinematic similarity of difference and differential equations with constant coefficients.