We investigate the size of the distance set determined by two subsets of finite dimensional vector spaces over finite fields. A lower bound of the size is given explicitly in terms of cardinalities of ...

Abstract This note gives a “Zorn’s Lemma” style proof that any two bases in a vector space have the same cardinality. The Monthly publishes articles, as well as notes and other features, about ...

How Google Converted Language Translation Into a Problem of Vector Space Mathematics To translate one language into another, find the linear transformation that maps one to the other.