This volume on matrix algebra and its companion volume on statistics are the first two volumes of the Econometric Exercises Series. The two books contain exercises in matrix algebra, probability, and statistics, relating to course material that students are expected to know while enrolled in an (advanced) undergraduate or a postgraduate course in econometrics.

When we started writing this volume, our aim was to provide a collection of interesting exercises with complete and rigorous solutions. In fact, we wrote the book that we — as students — would have liked to have had. Our intention was not to write a textbook, but to supply material that could be used together with a textbook. But when the volume developed we discovered that we did in fact write a textbook, be it one organized in a completely different manner. Thus, we do provide and prove theorems in this volume, because continually referring to other texts seemed undesirable. The volume can thus be used either as a self-contained course in matrix algebra or as a supplementary text.

We have attempted to develop new ideas slowly and carefully. The important ideas are introduced algebraically and sometimes geometrically, but also through examples. It is our experience that most students find it easier to assimilate the material through examples rather than by the theoretical development only.