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 ...

L. J. Ratliff, Jr., The Dimension of the Magic Square Vector Space, The American Mathematical Monthly, Vol. 66, No. 9 (Nov., 1959), pp. 793-795 ...

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.