Multiparameter perturbation theory of matrices and linear operators
| Autor: | Adam Parusinski, Guillaume Rond |
|---|---|
| Přispěvatelé: | Laboratoire Jean Alexandre Dieudonné (JAD), Université Côte d'Azur (UCA)-Université Nice Sophia Antipolis (... - 2019) (UNS), COMUE Université Côte d'Azur (2015-2019) (COMUE UCA)-COMUE Université Côte d'Azur (2015-2019) (COMUE UCA)-Centre National de la Recherche Scientifique (CNRS), Institut de Mathématiques de Marseille (I2M), Aix Marseille Université (AMU)-École Centrale de Marseille (ECM)-Centre National de la Recherche Scientifique (CNRS), ANR-17-CE40-0023,LISA,Géométrie Lipschitz des singularités(2017), Laboratoire Jean Alexandre Dieudonné (LJAD), Université Nice Sophia Antipolis (1965 - 2019) (UNS), COMUE Université Côte d'Azur (2015-2019) (COMUE UCA)-COMUE Université Côte d'Azur (2015-2019) (COMUE UCA)-Centre National de la Recherche Scientifique (CNRS)-Université Côte d'Azur (UCA) |
| Jazyk: | angličtina |
| Rok vydání: | 2018 |
| Předmět: |
Pure mathematics
Monomial Mathematics::Commutative Algebra Applied Mathematics General Mathematics 010102 general mathematics Commutative Algebra (math.AC) Mathematics - Commutative Algebra 01 natural sciences Normal matrix Functional Analysis (math.FA) Mathematics - Functional Analysis Matrix (mathematics) Mathematics - Algebraic Geometry Discriminant Singular value decomposition FOS: Mathematics [MATH.MATH-AG]Mathematics [math]/Algebraic Geometry [math.AG] 0101 mathematics Perturbation theory Algebraic Geometry (math.AG) Unit (ring theory) ComputingMilieux_MISCELLANEOUS Mathematics Characteristic polynomial |
| Zdroj: | Transactions of the American Mathematical Society Transactions of the American Mathematical Society, American Mathematical Society, 2020, 373 (4), pp.2933-2948. ⟨10.1090/tran/8061⟩ Transactions of the American Mathematical Society, 2020, 373 (4), pp.2933-2948. ⟨10.1090/tran/8061⟩ |
| ISSN: | 0002-9947 1088-6850 |
| Popis: | We show that a normal matrix $A$ with coefficient in $\mathbb C[[X]]$, $X=(X_1, \ldots, X_n)$, can be diagonalized, provided the discriminant $\Delta_A $ of its characteristic polynomial is a monomial times a unit. The proof is an adaptation of the algorithm of proof of Abhyankar-Jung Theorem. As a corollary we obtain the singular value decomposition for an arbitrary matrix $A$ with coefficient in $\mathbb C[[X]]$ under a similar assumption on $\Delta_{AA^*} $ and $\Delta_{A^*A} $. We also show real versions of these results, i.e. for coefficients in $\mathbb R[[X]]$, and deduce several results on multiparameter perturbation theory for normal matrices with real analytic, quasi-analytic, or Nash coefficients. Comment: 15 pages - to appear in Trans. Amr. Math. Soc |
| Databáze: | OpenAIRE |
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