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arXiv · 1311.1144

An informal introduction to perturbations of matrices determined up to similarity or congruence

Lena Klimenko·Vladimir V. Sergeichuk
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Abstract

The reductions of a square complex matrix A to its canonical forms under transformations of similarity, congruence, or *congruence are unstable operations: these canonical forms and reduction transformations depend discontinuously on the entries of A. We survey results about their behavior under perturbations of A and about normal forms of all matrices A+E in a neighborhood of A with respect to similarity, congruence, or *congruence. These normal forms are called miniversal deformations of A; they are not uniquely determined by A+E, but they are simple and depend continuously on the entries of E.

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Lena Klimenko, Vladimir V. Sergeichuk. 2013-12-14. An informal introduction to perturbations of matrices determined up to similarity or congruence. https://arxiv.org/abs/1311.1144

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