> Preface

# Preface to Matrix Algebra Using MINImal MATlab Joel W. Robbin

There is, I am told, a small town in Middle America populated entirely by people engaged in the writing of textbooks of elementary linear algebra. I should like to explain what motivates those tormented souls.

In most colleges the first course in linear algebra provides the student with her/his first contact with material that requires mathematical literacy. Linear algebra cannot be understood without a partial mastery of the lingo mathematicians use to describe their subject. The student must master hard words like if, unique, for all , and (hardest of all) there exists. To one who knows these words, the subject is almost trivial; to the uninitiated, it is impossibly arcane. The course in linear algebra represents a kind of watershed. Its survivors will love mathematics and will exhibit a kind of clarity of thought that will serve them well in almost any future scientific endeavor. Moreover, mathematical literacy isn't much different from the other kind. The first course in linear algebra prepares one for the modern world better than any other course in the college curriculum. So this is why there are so many textbooks in linear algebra: the subject is important.

The book has ambitious objectives. It aims to teach mathematical literacy by providing a careful treatment of set theoretic notions and elementary mathematical proofs. It aims to develop geometric intuition via low dimensional examples. It gives a complete treatment of the fundamental normal form theorems of matrix algebra. It fully integrates the computer into the course by describing the basic algorithms in the computer language {\em Matlab} and by providing computer exercises that utilize new pedagogical techniques. It contains enough material for a year long course such as the 340-443 sequence at the University of Wisconsin. The first six chapters of the book can be used in a course which follows the recommendations of NSF's Linear Algebra Curriculum Study Group (see D. Carlson, C. R. Johnson, D. C. Lay, A. D. Porter: The linear algebra curriculum study group recommendations for the first course in linear algebra, College Math Journal 24 Jan. 1993, pp 41-46.

An old DOS version of the computer program MINIMAT is provided free with this book. A Java version as well as a version for the Macintosh can be downloaded from the author's home page:

http://www.math.wisc.edu/~robbin

This program is upward compatible with commercial versions such as PC-Matlab published by the Mathworks and Student Edition of Matlab published by Prentice-Hall. MINIMAT contains only those features which are useful in teaching an elementary course. All the programs listed in the text are duplicated in .m files supplied on the distribution diskette. or can be dowloaded from my website. These .m files work with most versions of Matlab as well. In particular, they have been tested with The Student Edition of Matlab.

Conversations with many colleagues, too numerous to mention, influenced this book. Typically, one of them would say something like, Oh, the students just don't understand X'', and I would make X an example or exercise in the book. The Warmup'' on page 2 is based on the first lecture David Fowler gives whenever he teaches this subject. The idea for numbering the theorems (Theorem~99B is the second theorem on Page 99) is due to Anatole Beck. I would like to thank Anatole Beck, Sufian Huseinni, Jerry Keisler, Arnie Miller, Rod Smart, and Dietrich Uhlenbrock, for using preliminary versions of these materials in their Math 340 classes at UW. Their experiences proved invaluable. I also benefitted from conversations with Carl de Boor. Al Letarte found many typographical errors while preparing his study guide for the UW extension course in matrix algebra.

My family did more than provide emotional support and tolerance. My wife Alice Robbin did a magnificent job of proof reading, and my daughter Rachel Robbin provided significant insight into how students learn by allowing me to help her with her math homework.

Thanks also go to IBM's Project Trochos, which provided the IBM-AT on which MINIMAT was originally developed.

Jorl W. Robbin
Department of Mathematics
University of Wisconsin