Research Seminar in Mathematics - Versal deformations of matrices
16 September 2022 13:15 Zoom
Please contact Andrii Dmytryshyn if you have any questions regarding this seminar series.
Speaker
Andrii Dmytryshyn, Örebro University.
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Meeting ID: 626 4959 5008
Passcode: 320339
Abstract
Jordan canonical form for matrices is well known and studied with various purposes but reduction to this form is an unstable operation: both the corresponding canonical form and the reduction transformation depend discontinuously on the entries of an original matrix. This issue complicates the use of the canonical form for numerical purposes. Therefore V.I. Arnold introduced a normal form to which an arbitrary family of matrices A' close to a given matrix A can be reduced by similarity transformation smoothly depending on the entries of A’. He called such a normal form a versal deformation of A.
In this presentation we will discuss versal deformations and their use in investigation of possible changes in canonical forms (eigenstructures), reduction of unstructured perturbations to structured perturbations, and codimension computations.
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