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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 $ 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 \ne 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.


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DOI: https://doi.org/10.1090/S0002-9939-1988-0947649-X
Article copyright: © Copyright 1988 American Mathematical Society

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