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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.


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.

Item Type:Article
Additional Information:
Keywords:Pencils of matrices, Singularities, Determinacy.
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Record Created:27 Apr 2007
Last Modified:08 Apr 2009 16:30

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