J.W. Bruce
On families of square matrices
Bruce, J.W.; Tari, F.
Authors
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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