Chapter 3 - Elements of linear algebra

Abstract

Linear algebra is another fundamental tool of mathematical economics, under several respects. Within this chapter we will show how Excel can deal with the basic linear algebra calculus via the built-in matrix functions. Then, also some key theorems of linear algebra will be explained and applied. A special attention should be devoted to the linear systems of simultaneous equations because of the underlying theorems involved in their resolutions. Linear algebra is used a lot in mathematical economics (and econometrics as well) because several models assume the linearity in the economic relations, together with the assumption that these linear relations are all interconnected each other, leading to using an important theory of linear algebra which is represented by the systems of linear equations. Some key theorems of linear algebra are used in the areas of mathematical economics, like the systems of linear differential equations or like the optimization of multivariate functions. In economics, two areas where the linear algebra is typically used are the theory of macroeconomics and the theory of economic policy, where the economic aggregates are always modeled as linear equations. Also, the input–output models use linear algebra to explain the interrelations among the various economic industries. In the theory of microeconomics, linear algebra can be used instead to study the equilibrium in the markets. This chapter will explain some models as well, regarding all this.