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

Author:
L. N. Vaserstein

Journal:
Proc. Amer. Math. Soc. **103** (1988), 741-746

MSC:
Primary 18F25; Secondary 19B10

DOI:
https://doi.org/10.1090/S0002-9939-1988-0947649-X

MathSciNet review:
947649

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Abstract: It is shown that any by 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 for real-valued functions; moreover, if this is the case, the number of operations can be bounded by a constant depending only on and the dimension of the space. For real functions and , 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.

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DOI:
https://doi.org/10.1090/S0002-9939-1988-0947649-X

Article copyright:
© Copyright 1988
American Mathematical Society