# Tropical Laurent series, their tropical roots, and localization results for the eigenvalues of nonlinear matrix functions

@article{Porzio2021TropicalLS, title={Tropical Laurent series, their tropical roots, and localization results for the eigenvalues of nonlinear matrix functions}, author={Gian Maria Negri Porzio and Vanni Noferini and Leonardo Robol}, journal={ArXiv}, year={2021}, volume={abs/2107.07982} }

Tropical roots of tropical polynomials have been previously studied and used to localize roots of classical polynomials and eigenvalues of matrix polynomials. We extend the theory of tropical roots from tropical polynomials to tropical Laurent series. Our proposed definition ensures that, as in the polynomial case, there is a bijection between tropical roots and slopes of the Newton polygon associated with the tropical Laurent series. We show that, unlike in the polynomial case, there may be…

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