The AROMATH seminar will usually happen on Tuesday at 10h30-11h30 every two weeks, except for a few deviations.
The presentations will typically take place at Inria Sophia Antipolis, Byron Blanc 106, and also online.
To join online, at https://cutt.ly/aromath or with a web browser at https://cutt.ly/aromath-web
use meeting ID: 828 5859 7791, passcode: 123
Adam Parusinski – Multiparameter perturbation theory of matrices and linear operators
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28 October 2020
We consider perturbation theory of normal matrices whose entries depend on one or many parameters. We show that a normal matrix $A$ with coefficients in the ring of formal power series $\C[[X]]$, $X=(X_1, \ldots, X_n)$, can be diagonalized, provided the discriminant $\Delta_A $ of its characteristic polynomial is a monomial times a unit (the assumption always satisfied in the case of one parameter). The proof is an adaptation of our proof of the Abhyankar-Jung Theorem. As a corollary we obtain the SVD for an arbitrary matrix $A$ with coefficients in $\C[[X]]$ under a similar assumption on $\Delta_{AA^*} $ and $\Delta_{A^*A} $. We also show the real versions of these results, i.e. for coefficients in $\R[[X]]$. (joint work with Guillaume Rond, AMU, https://arxiv.org/abs/1807.04242)
