My World of Linear Algebra


Welcome. So why this page? In my own work I've encountered many flavors of mathematics (group theory, ring theory, commutative algebra, applied mathematics and numerical analysis, etc) and a common thread throughout my mathematical experiences has been linear algebra. I've taught the subject many times, and it seems that students are always teaching me something new about the subject as well. So, as you can see, I think linear algebra is a really great subject. It seems to be connected to everything. In fact, I think for many science/math students it's every bit as important as calculus.


The original impetus for this page was to provide a viewing of a textbook that I've been writing about linear algebra off and on since about 1992. I've used a number of tools in the linear algebra course that I've taught, starting with the venerable HP-28 in 1987 and moving up to advanced computer algebra systems (CAS) like Maple and Mathematica, and matrix algebra systems (MAS), like Matlab and Octave. I would like to share some of the resources that I've found and/or developed in conjunction with my text. I used these resources in many other courses I taught, primarily numerical analysis and differential equations, and I hope that others will find uses for them in their own courses. Some of the tools are rather dated, so user beware.

In addition, this Web page is also somewhat dated as that I retired in 2010, so it's a bit rough at the edges. Nonetheless, I'll be adding features and some new pages, so linear algebra fans, stay tuned! BTW, if you do find any of the resources that I've created here useful, I would appreciate hearing about it.

I have some new information to share regarding my textbook: It has continued to enjoy some success after a decade and the folks at Springer-Verlag felt that a new edition would be a worthwhile endeavor. To this end I have just completed a revision of the textbook. For information about this revision click on the first link below.

Linear Algebra Resources


Random Notes and FAQ


Here are some random notes about topics of interest, comments by users and answers to a few questions I've been asked.
  1. What's Octave? If you've ever heard of Matlab, you have a good idea what Octave is. This superb program has been developed by John Eaton and others over the past two decades under the GNU License, so it is publicly available for free. It runs under many platforms including some versions of Windows, macOS and Linux. It was developed for instructional purposes, but I've found it to be very useful for research as well. If you're looking for a Matlab clone, forget it: Octave is close to Matlab in functionality (there are even some features that Matlab doesn't have), but it doesn't have some of the advanced features of Matlab. Matlab is a computing standard for numerical experimentation and research. I've written a lot of (mostly Matlab compatible) Octave code, and if you want to see more than linear algebra, click on the Public Files button. If you're interested in getting a copy of Octave, click on Octave Home Page.
  2. What's LyX and what does it have to do with teaching? Glad you asked. This is a program that not-enough-people know about. It is a polished GUI front end to Latex that runs on Windows, macOS and various flavors of Unix and Linux. It's not exactly a WYSIWYG, but a WYSIWYM ("what you see is what you mean"). I use it all the time. It can even import (correctly written) native Latex. I used this feature to import my linear algebra book, which I originally wrote in Latex. When I want a pure Latex file, I simply export my .lyx file. This is no big deal for LyX because Latex is the engine under the hood for generating view and print files. For that matter, if I want an html version, that kind of export is available as well. Anyone who is familiar with Scientific Word will be immediately comfortable with this program. If you're interested in getting a copy of LyX, click on the LyX Home Page.