Periods of Linear Combinations of Vectors

Abstract

In this paper we attack four mutually related problems about the periods of linear combinations of vectors. The first problem is to find all the possible numbers that can be the T-period of $$u+v$$u+v when the T-period of u and the T-period of $$v$$v are known; where T is a linear operator on a vector space. The other three problems lead to some consequences of the first result.