Linear Gears for Asset Pricing

The purpose of this paper is to use a few simple results of linear algebra to derive some properties of a general asset pricing model. Since one can apply essentially the same techniques in both cases, we start by considering a traditional asset pricing model and then show how to extend the reasoning to a more general model. In order to present our results, we need to state several assumptions that are customarily made in the studies of finance. Unless explicit mention is made, we maintain these assumptions throughout this work although some of them could be relaxed with little effort.