The asymptotic behavior of the singular values of matrix powers and applications Original Research Article

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 → ∞. One of the main results gives for each k an explicit construction of a sequence of the form (a(k)nnøl(k))∞n=1 which is equivalent to the sequence (sk(An))∞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.