ABSTRACT
This chapter contains a brief review of linear algebra and an introduction to convex analysis and its applications to linear programming. It briefly reviews several topics from elementary linear algebra and matrix theory. These topics include vector spaces, matrices, elementary row operations and the Gauss-Jordan method of elimination. Some of the concepts from linear algebra are related to new concepts in convex analysis. The chapter deals with Gaussian elimination, LU-decompositions, and basic solutions of systems of equations. When the rows are permuted in the Gaussian elimination procedure to allow the largest possible pivot element, the technique is known as partial pivoting. The chapter illustrates the usefulness of convex analysis as a tool in describing the solutions of the linear programming problem. It discusses the use of slack variables to change a linear inequality constraint into a linear equality constraint.
