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arXiv · 2212.00713

Analytic, Differentiable and Measurable Diagonalizations in Symmetric Lie Algebras

Emanuel Malvetti·Gunther Dirr·Frederik vom Ende·Thomas Schulte-Herbrüggen
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Abstract

We generalize several important results from the perturbation theory of linear operators to the setting of semisimple orthogonal symmetric Lie algebras. These Lie algebras provide a unifying framework for various notions of matrix diagonalization, such as the eigenvalue decomposition of real symmetric or complex Hermitian matrices, and the real or complex singular value decomposition. Concretely, given a path of structured matrices with a certain smoothness, we study what kind of smoothness one can obtain for the corresponding diagonalization of the matrices.

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BibTeXRIS

Emanuel Malvetti, Gunther Dirr, Frederik vom Ende, Thomas Schulte-Herbrüggen. 2022-12-01. Analytic, Differentiable and Measurable Diagonalizations in Symmetric Lie Algebras. https://arxiv.org/abs/2212.00713

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