A First Course In Linear Algebra

A First Course in Linear Algebra by Robert A. Beezer Department of Mathematics and Computer Science University of Puget Sound Version 0.70 January 5, 2006 c 2004, 2005, 2006 c 2004, 2005, 2006 Robert A. Beezer. Copyright Permission is granted to copy, distribute and/or modify this document under the terms of the GNU Free Documentation License, Version 1.2 or any later version published by the Free Software Foundation; with the Invariant Sections being “Preface”, no Front-Cover Texts, and no Back-Cover Texts. A copy of the license is included in the section entitled “GNU Free Documentation License”. Most recent version can be found at http://linear.ups.edu/. Preface This textbook is designed to teach the university mathematics student the basics of the subject of linear algebra. There are no prerequisites other than ordinary algebra, but it is probably best used by a student who has the “mathematical maturity” of a sophomore or junior. The text has two goals: to teach the fundamental concepts and techniques of matrix algebra and abstract vector spaces, and to teach the techniques associated with understanding the definitions and theorems forming a coherent area of mathematics. So there is an emphasis on worked examples of nontrivial size and on proving theorems carefully. This book is copyrighted. This means that governments have granted the author a monopoly — the exclusive right to control the making of copies and derivative works for many years (too many years in some cases). It also gives others limited rights, generally referred to as “fair use,” such as the right to quote sections in a review without seeking permission. However, the author licenses this book to anyone under the terms of the GNU Free Documentation License (GFDL), which gives you more rights than most copyrights. Loosely speaking, you may make as many copies as you like at no cost, and you m