Reduction of a matrix depending on parameters to a diagonal form by addition operations

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Abstract

It is shown that any n by n matrix with determinant 1 whose entries are real or complex continuous functions on a finite dimensional normal topological space can be reduced to a diagonal form by addition operations if and only if the corresponding homotopy class is trivial, provided that n≠2 for real-valued functions; moreover, if this is the case, the number of operations can be bounded by a constant depending only on n and the dimension of the space. For real functions and n = 2, we describe all spaces such that every invertible matrix with trivial homotopy class can be reduced to a diagonal form by addition operations as well as all spaces such that the number of operations is bounded.

Original languageEnglish (US)
Pages (from-to)741-746
Number of pages6
JournalProceedings of the American Mathematical Society
Volume103
Issue number3
DOIs
StatePublished - Jul 1988

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All Science Journal Classification (ASJC) codes

  • Mathematics(all)
  • Applied Mathematics

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