A reduced form for perturbed matrix polynomials
Claude-Pierre Jeannerod · 2002
We show that every perturbation A(λ, ε) of an n x n matrix polynomial A(λ) such that det A(λ) = λm with m ≤ n can be reduced by equivalence transforms to a perturbed matrix polynomial whose leading matrix has maximal Smith form. This yields a reduced form for square perturbed matrix polynomials from which one can easily recover all the eigenvalue leading terms of the form μεβ with β-1 ∈ ℕ*.