Abstract Using the axiom of choice, we prove a generalized converse of the well-known fact that if X is a finite-dimensional vector space, then any linear functional on X is continuous with respect to ...

Banach space theory, with its emphasis on complete normed vector spaces, provides the natural setting for addressing problems in functional analysis, differential equations and beyond.

Web Semantics: Language as vector space mathematics *Makes one wonder what it would sound like to simply speak vector space mathematics aloud, rather than bothering with human language.

For vector time series we compare the forecast efficiencies of two alternative approaches: first model and forecast and then form the linear combination, and first form the linear combination and then ...

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.