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On families of square matrices

  • J. W. Bruce (a1) (a2) and F. Tari (a3) (a4)

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.

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The research of the second author was partially supported by a CNPq grant.

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On families of square matrices

  • J. W. Bruce (a1) (a2) and F. Tari (a3) (a4)

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