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Conference Papers Year : 2002

A reduced form for perturbed matrix polynomials

Claude-Pierre Jeannerod
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Abstract

We show that every perturbation $A(\lambda, \epsilon)$ of an $n \times n$ matrix polynomial $A(\lambda)$ such that $\det A(\lambda) = \lambda^m$ with $m \le n$ 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 $\mu \epsilon^\beta$ with $\beta^{-1}\in\mathbb{N}^*$.
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Dates and versions

hal-03420227 , version 1 (09-11-2021)

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Claude-Pierre Jeannerod. A reduced form for perturbed matrix polynomials. International Symposium on Symbolic and Algebraic Computation (ISSAC), Jul 2002, Lille, France. pp.131-137, ⟨10.1145/780506.780523⟩. ⟨hal-03420227⟩
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