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The Order of Algebraic Linear Transformations

Published online by Cambridge University Press:  20 November 2018

Randee Putz
Randee Putz*
Affiliation:
Temple University, Philadelphia, Pennsylvania
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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 = (b1, …, bn) in En is algebraic if each coordinate bi is algebraic over the rationals. A linear transformation T: En → En 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: Kn → Kn.

Type
Research Article
Information
Canadian Mathematical Bulletin , Volume 13 , Issue 2 , June 1970 , pp. 277 - 278
Copyright
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