On simple singularities of skew-symmetric matrix families

In this paper we study analytic families of skew-symmetric matrices. We consider them up to-equivalence, i.e., up to parameter-dependent linear base changes and parameter changes. We obtain necessary existence conditions for simple families of this type in terms of number of parameters, matrix size...

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Bibliographic Details
Main Authors: Astashov, Evgeny, Abdrakhmanova, Nelly
Format: Conference Proceeding
Language:English
Subjects:
Canonical forms
Mathematical analysis
Matrices (mathematics)
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Summary:In this paper we study analytic families of skew-symmetric matrices. We consider them up to-equivalence, i.e., up to parameter-dependent linear base changes and parameter changes. We obtain necessary existence conditions for simple families of this type in terms of number of parameters, matrix size and 1-jet rank. We also present normal forms of skew-symmetric matrix families with 1-jet corank zero and one.
ISSN:0094-243X
1551-7616
DOI:10.1063/5.0162237