### 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 language | English (US) |
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Pages (from-to) | 741-746 |

Number of pages | 6 |

Journal | Proceedings of the American Mathematical Society |

Volume | 103 |

Issue number | 3 |

DOIs | |

State | Published - Jul 1988 |

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### All Science Journal Classification (ASJC) codes

- Mathematics(all)
- Applied Mathematics