### Economics and the Matrix

My title sounds like a new addition to the successful Matrix film series. Actually it is a cheap trick just to catch your attention!Matrix algebra is widely used in economics to write compactly and to manipulate simultaneous equation linear economic models. Although ordinary algebra works OK when there are only two or three equations to worry about, it becomes increasingly cumbersome and unwieldy as the number of equations in the system increases. This is where the methods of matrix algebra come into their own. You will find economists use matrices (the plural of matrix) not just to solve systems of linear equations, but also to obtain the "reduced form" of a model expressing the equilibrium values of the endogenous variables in terms of the exogenous ones, to manipulate input-output models that show the inter-relations between different sectors of the economy and to work with different estimators and test procedures in econometrics. It is therefore essential that all students of economics have a good grasp of at least the basics of matrix algebra and an understanding of how it is used in economics.

The recommended textbook for my course on further mathematics for economists at Portsmouth is Fundamental Methods of Mathematical Economics by Alpha C Chiang and Kevin Wainwright. However this book is rather expensive and you might try to look for a second-hand copy of an earlier edition of this book, when it was just authored by Chiang.

Alternatively you might look for some free notes and material online. I have tracked down a few helpful sites for you - see below. But however much reading material you have the only way to learn maths is to do it. So if you are taking my course please make sure that you work on the problem sheets I have prepared (if you have mislaid them you can get hold of them from the unit website) and come to all my classes. If you are not on my course and have just stumbled on this blog because of an interest in mathematics, I hope that you find something interesting here!

Some useful links on matrix algebra

- Matrix algebra notes from Aidan Kane at the National University of Galway, Ireland
- Matrix Algebra: An introduction to the theory and application of matrices from Morello Publishing Ltd
- notes from D S G Pollock
- Matrix Algebra Review from Eric Zivot at the University of Washington
- SOS MATHematics website
- Matrix algebra notes from Phillip Wood in Missouri
- Matrix algebra notes from xycoon.com
- Matrix algebra material from Stefan_Waner including

a matrix algebra interactive tool and a True/False quiz