On Families of Square Matrices

J.W. Bruce, F. Tari

    Research output: Contribution to journalArticle

    6 Citations (Scopus)

    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. 2000 Mathematics Subject Classification 58K40, 58K50, 58K60, 32S25.
    Original languageEnglish
    Pages (from-to)738-762
    JournalProceedings of the London Mathematical Society
    Volume89
    Issue number3
    DOIs
    Publication statusPublished - 2004

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