On Families of Square Matrices

Bruce, J.W. and Tari, F. (2004) On Families of Square Matrices. Proceedings of the London Mathematical Society, 89 (3). pp. 738-762. ISSN 0024-6115 DOI https://doi.org/10.1112/S0024611504014911

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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. 2000 Mathematics Subject Classification 58K40, 58K50, 58K60, 32S25.

Item Type: Article
Subjects: Q Science > QA Mathematics
Date Deposited: 04 Dec 2010 19:42
URI: http://repository.edgehill.ac.uk/id/eprint/1536

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