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 ...

Linear operators form the cornerstone of analysis in Banach spaces, offering a framework in which one can rigorously study continuity, spectral properties and stability. Banach space theory, with its ...

We introduce a principal support vector machine (PSVM) approach that can be used for both linear and nonlinear sufficient dimension reduction. The basic idea is to divide the response variables into ...

*Makes one wonder what it would sound like to simply speak vector space mathematics aloud, rather than bothering with human language. "Computer science is changing the nature of the translation of ...