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On families of square matrices

Bruce, J.W.; Tari, F.

Authors

J.W. Bruce

F. Tari



Abstract

In this paper we classify families of square matrices up to the following natural equivalence. Thinking of these families as germs of smooth mappings from a manifold to the space of square matrices, we allow arbitrary smooth changes of co-ordinates in the source and pre- and post- multiply our family of matrices by (generally distinct) families of invertible matrices, all dependent on the same variables. We obtain a list of all the corresponding simple mappings (that is, those that do not involve adjacent moduli). This is a non-linear generalisation of the classical notion of linear systems of matrices. We also make a start on an understanding of the associated geometry.

Citation

Bruce, J., & Tari, F. (2004). On families of square matrices. Proceedings of the London Mathematical Society, 89(3), 738-762. https://doi.org/10.1112/s0024611504014911

Journal Article Type Article
Publication Date 2004
Deposit Date Apr 27, 2007
Journal Proceedings of the London Mathematical Society
Print ISSN 0024-6115
Electronic ISSN 1460-244X
Publisher Wiley
Peer Reviewed Peer Reviewed
Volume 89
Issue 3
Pages 738-762
DOI https://doi.org/10.1112/s0024611504014911
Keywords Pencils of matrices, Singularities, Determinacy.

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