Duality

Abstract

Duality is yet another of those fundamental concepts that finds applications in many areas of mathematics. In classical geometry a duality exists between points and lines, the simplest expression of which is the observation that two straight lines intersect in a single point and two points are joined by a single straight line. More sophisticated geometric examples can be found where theorems concerning the co-linearity of points are dual to apparently quite unrelated theorems involving the co-incidence of lines. In mathematical economics the duality implicit in certain economic systems is reflected in the mathematical models of those systems. Since problems of linear programming are frequently derived from economic systems the duality exhibited by the general LP problem is the mathematical expression of the underlying economic duality.