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The Order of Algebraic Linear Transformations
Published online by Cambridge University Press: 20 November 2018
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In this paper we extend the results of an earlier note [1].
Definition. Let E be an extension field of the rationals. A vector v = (b 1, …, b n ) in E n is algebraic if each coordinate b i is algebraic over the rationals. A linear transformation T: E n → E n is algebraic if T(v) is an algebraic vector for every algebraic vector v.
Definition. The degree of an algebraic linear transformation T, denoted by deg T, is the minimum of [K:Q] taken over all finite algebraic extensions K of the rationals Q such that T: K n → K n .
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- Copyright © Canadian Mathematical Society 1970
References
1.
Putz, Randee, An estimate for the order of rational matrices, Canad. Math. Bull. 10 (1967), 459-461.Google Scholar
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