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A reduced form for perturbed matrix polynomials

Claude-Pierre Jeannerod 1 
1 ARIC - Arithmetic and Computing
Inria Grenoble - Rhône-Alpes, LIP - Laboratoire de l'Informatique du Parallélisme
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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https://hal.inria.fr/hal-03420227
Contributor : Claude-Pierre Jeannerod Connect in order to contact the contributor
Submitted on : Tuesday, November 9, 2021 - 9:39:08 AM
Last modification on : Tuesday, October 25, 2022 - 4:19:03 PM
Long-term archiving on: : Thursday, February 10, 2022 - 6:18:46 PM

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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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