Geodesic
The Order of Algebraic Linear Transformations
Canadian mathematical bulletin, Tome 13 (1970) no. 2, pp. 277-278

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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 . 
Putz, Randee. The Order of Algebraic Linear Transformations. Canadian mathematical bulletin, Tome 13 (1970) no. 2, pp. 277-278. doi: 10.4153/CMB-1970-055-x
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[1] 1. Putz, Randee, An estimate for the order of rational matrices, Canad. Math. Bull. 10 (1967), 459-461. Google Scholar

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