Forms of Multidimensional Relationships

Abstract

This chapter briefly considers the question of extending the traditional scalar methods of dimensional analysis,⁵⁶ used for deriving the forms of scalar relationships, to methods for deriving the forms of multidimensional equations; it is intended to be exploratory and provocative. As a multidimensional form of dimensional analysis, we want to develop techniques of multidimensional analysis in which the dimensional structures of vectors and matrices are used not just in checking consistency and expressing dimensional forms, but also for deriving new results.

Dimensional analysis is essentially of the nature of an analysis of an analysis. —Percy W. Bridgman