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QABE_Notes05

# QABE_Notes05 - QABE Lecture 5 Matrices I Maths by...

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QABE Lecture 5 Matrices I: Maths by Arrangement School of Economics, UNSW 2011 Contents 1 Introduction 1 2 Terminology 2 2.1 Special matrices . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3 3 Operations 4 3.1 Addition & subtraction . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5 3.2 Scalar multiplication . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5 4 Matrix Multiplication 6 4.1 Working it out . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6 1 Introduction We now move to a few studies in the world of matrices . 1 Think about going on a trip to a very special island, like the Galapogos Islands off the coast of South America. The place is so special and different that it may even have different laws of nature operating on it. Now this might be a very scary thought. Chances are, the scariness comes directly from the fact that the world might operate so differently from the one that we are familiar with, that we won’t know what to do, how to behave, what to expect. A natural reaction is to try to find ways of doing things on the special island that we are used to doing back home. This kind of journey is exactly what we’ll be embarking on in this lecture. We’ll venture into the world of Matrices , and immediately start looking for mathematical elements that we are used to in our ‘normal’ (scalar) world, so as to feel more comfortable in the new place. The important implication of this journey is firstly, that we shouldn’t expect to be able to do our ‘old’ maths in the new world, and secondly, that we must recognise which world we are working in! Or else, we may try to apply a rule to the wrong world that predictably will give rise to all kinds of unintended consequences. For some people, this area can cause a lot of trouble, since in a number of cases, the way that we perform operations (e.g. subtraction, addition, multiplication) on matrices gives rise to different outcomes than with just, well, numbers on their own. In times such 1 Note: in the prepartion of this section on Matrices, reference has been made to the excellent text Linear Algebra (3rd Ed.) by Fraleigh and Beauregard (FB) (1995). By noting this, you may feel tempted

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