Lattices and dimensional representations: matrix decompositions and ordering structures

This paper is concerned with some methods that attempt to provide simultaneous representation of dual relationships, such as ties of membership that connect persons and groups, or connections between organizations and agendas. We focus on vector space and lattice representations, and on techniques for simplifying the structure of dual networks. We demonstrate some fundamental similarities among these approaches. © 2002 Elsevier Science B.V. All rights reserved.