The behavior of the complete eigenstructure of a polynomial matrix under a generic rational transformation
Vanni Noferini · Electronic Journal of Linear Algebra · 2012
Given a polynomial matrix P (x) of grade g and a rational function x(y) = n(y)/d(y), where n(y) and d(y) are coprime nonzero scalar polynomials, the polynomial matrix Q(y) := [d(y)] g P (x(y)) is defined.The complete eigenstructures of P (x) and Q(y) are related, including characteristic values, elementary divisors and minimal indices.A theorem on the matter, valid in the most general hypotheses, is stated and proved.