Matrix Algebra Using MINImal MATlab

Joel W. Robbin

In most colleges the first course in linear algebra provides the student with her/his first contact with material that requires

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:

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:

This program is upward compatible with commercial versions such as

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

Jorl W. Robbin

Department of Mathematics

University of Wisconsin

Madison, Wisconsin 53706

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