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A first course in Linear Algebra(Free Text Book)


This page contains more explanation about this project. The preface from Version 2.00 contains more specific details about how and why I wrote this book and is a good place to begin. The News section below lists some of the milestones in the development of the book, while greater detail can be found in the current Change Log, which is available off the Download page. The Download page also includes a link to two sample sections.



VLA - Visual Linear Algebra


VLA is a linear algebra software package developed for MA 211 (Applied Mathematics I) and MA 213 (Applied Mathematics III) which are part of the Rose-Hulman Foundation Coalition Sophmore Engineering Curriculum.

The software was developed during the summer of 1996 by Brad North (EE junior at Rose-Hulman), Roger Lautzenheiser (Mathematics faculty) , and Yosi Shibberu (Mathematics faculty) . The authors would like to thank the National Science Foundation (Foundation Coalition, an Engineering Education Coalition) for its support.





Thanks to Gene Herman for compiling this Glossary as part of his Math 215 Homepage at Grinnell University.



Matrix Analysis and Applied Linear Algebra


This book evolved over a period of several years through many different courses populated by hundreds of undergraduate and graduate students. To all my students and colleagues who have offered suggestions, corrections, criticisms, or just moral support, I offer my heartfelt thanks, and I hope to see as many of you as possible at some point in the future so that I can convey my feelings to you in person. I am particularly indebted to my students for conversations and suggestions that led to several improvements-special thanks goes to Michele Benzi. All writers are influenced by people who have written before them, and for me these writers include Gil Strang, Jim Ortega, Gene Golub, Charlie Van Loan, Leonid Mirsky, Ben Noble, Roger Horn, Charlie Johnson, Peter Lancaster, Paul Halmos, Franz Hohn, Richard Bellman, Nick Rose, and Pete Stewart-thanks for lighting the path. I want to offer particular thanks to Richard J. Painter and Franklin A. Graybill, two exceptionally fine teachers, for giving a rough Colorado farm boy a chance to pursue his dreams. Finally, neither this book nor anything else I have done in my career would have been possible without the love, help, and unwavering support from Bethany, my friend, partner, and wife. Her multiple readings of the manuscript and suggestions were invaluable. I dedicate this book to Bethany and our children, Martin and Holly, to our granddaughters, Margaret and Allison, and to the memory of my parents, Carl and Louise Meyer.



Introduction to Matrix Algebra


Autar K Kaw, Professor, University of South Florida

Copyright (c) 2007, Autar K Kaw. All rights reserved

This book is written primarily for students who

  • are at freshman level or
  • do not take a full course in Linear/Matrix Algebra, or
  • are wanting a contemporary and applied approach to Matrix Algebra.

I am making this book available FREE of charge at this time. If you use this book, I would like your comments for future editions of the e-book.

This book is copyrighted under U.S. Copyright Law. The author grant you the right to download and print it for your personal use or for non-profit instructional use. Any other use, including copying, distributing or modifying the work for commercial purposes, is subject to the restrictions of U.S. and international Copyright Laws.




Elements of Abstract and Linear Algebra


Author : Edwin H. Connell

This is a foundational textbook on abstract algebra with emphasis on linear algebra. You may download parts of the book or the entire textbook. It is provided free online in PDF, DVI, postscript, and gzipped postscript.

Please read some words from the author first.

Join the revolution in education! Write a supplement to this book and put it online.

Participate in and contribute to a forum on abstract and linear algebra. Ask questions, give answers, and make comments in a worldwide classroom with the internet as blackboard.



History Topics Index


JOC/EFR August 2006

University of St Andrews,Scotland

Abstract linear spaces

Matrices and determinants




On the Centrality of Linear Algebra in the Curriculum


Author : Carl C. Cowen

Remarks on receiving the Deborah and Franklin Tepper Haimo Award for Distinguished College or University Teaching of Mathematics, San Diego California, January 1997.

  • Introduction
  • A Little History
  • The Reform of the Linear Algebra Course
  • The Role of the Computer in the Classroom
  • References
While this is an opportunity for me to lay out my "secrets" for successful teaching, I have too few secrets and they are too well known for me to talk for more than a few minutes about them.



Linear Algebra Gems: Assets for Undergraduate Mathematics


edited by David Carlson, Charles R. Johnson, David C. Lay, and A. Duane Porter

Reviewed by Michele Intermont

Around 1990, the teaching of linear algebra came under examination, following the trend of calculus reform. The Linear Algebra Curriculum Study Group has been a dominant voice in leading the discussion since that time. The group, under the capable editorship of David Carlson, Charles Johnson, David Lay and Duane Porter, has once again provided a valuable resource for revitalizing one of the most basic courses in the math curriculum with this publication.

Having just finished teaching linear algebra for the first time last spring, and preparing to embark on my second opportunity, I was delighted to find Linear Algebra Gems: Assets for Undergraduate Mathematics, just before the start of classes. As with most who teach this course, I imagine, I found that only some of my students were mathematics majors. Many were computer science majors, some were economics majors, and several were undecided about which of these fields to pursue. When I picked up the book, I expected to find some ideas not only about the topics in the course, but also some reflections on the relevance of linear algebra outside of mathematics. I'm not sure where I could have gotten the idea that the book would provide some motivation to give my students; that's clearly not something the editors were attempting to do in this volume. (In fact, as mentioned below, there are such articles in a different MAA volume). But I was definitely rewarded in the mathematics I found.



LAVA : Linear Algebra Visualization Assistant



Welcome to LAVA, the Linear Algebra Visualization Assistant.

This interactive toolkit is designed to introduce concepts usually covered in a first course in linear algebra. The topics are presented in an informal, casual manner. The student is periodically asked questions designed to stimulate him or her to review previous material, reflect over material just presented, or to consider alternative approaches. The feedback from the questions is immediate and usually offers extended explantion tailored to address reason why an correct or incorrect answer was selected.

Since abstract concepts in mathematics are often best understood by forming an analogy with something concrete, LAVA makes use of interactive applets designed to foster a geometrical understanding of the concepts it presents. Often, this means that we are restricted to linear systems of two or three equations and to matrices of cooresponding size. However, once concepts such as linear independence and eigenvectors are understood in these simple, easy-to-visualize situations, it becomes much easier to work with higher dimensional problems, or even with vector spaces other than Rn.



* IMAGE - ILAS' Bulletin
* Electronic Journal of Linear Algebra
* Elsevier

ILAS Educational

Steve Leon (Chair)
Luz De Alba
Guershon Harel
David Lay
Sang-Gu Lee

ILAS Executive

* President
Stephen Kirkland
* Vice-President
Chi-Kwong Li
* Secretary/Treasurer
Leslie Hogben