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Multiparameter perturbation theory of matrices and linear operators. (English) Zbl 1440.15009

The authors use an approach based on the algorithm of a proof of the Abhyankar-Jung theorem to obtain a sufficient condition for a normal matrix with coefficients in \(\mathbb{C}[X_1,\cdots, X_n]\) to be diagonalized. The condition is related to the discriminant of the characteristic polynomial of the normal matrix. Particular results for real analytic, quasi-analytic or Nash coefficients are derived.

MSC:

15A23 Factorization of matrices
15A18 Eigenvalues, singular values, and eigenvectors
15A20 Diagonalization, Jordan forms
15A21 Canonical forms, reductions, classification
13F25 Formal power series rings
14P20 Nash functions and manifolds
47A55 Perturbation theory of linear operators

Citations:

Zbl 1268.13008
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References:

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