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# A Reduction Algorithm for Matrices Depending on a Parameter

Abstract : In this article, we study square matrices perturbed by a parameter $\epsilon$. An efficient algorithm computing the $\epsilon$-expansion of the eigenvalues in formal Laurent-Puiseux series is provided, for which the computation of the characteristic polynomial is not required. We show how to reduce the initial matrix so that the Lidskii-Edelman-Ma perturbation theory can be applied. We also explain why this approach may simplify the perturbed eigenvector problem. The implementation of the algorithm in the computer algebra system Maple has been used in a quantum mechanics context to diagonalize some perturbed matrices and is available.
Document type :
Conference papers

https://hal.inria.fr/hal-03419442
Contributor : Claude-Pierre Jeannerod Connect in order to contact the contributor
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### File

JeaPfl1999.pdf
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### Identifiers

• HAL Id : hal-03419442, version 1

### Citation

Claude-Pierre Jeannerod, Eckhard Pflügel. A Reduction Algorithm for Matrices Depending on a Parameter. International Symposium on Symbolic and Algebraic Computation (ISSAC), Jul 1999, Vancouver, Canada. ⟨hal-03419442⟩

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