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 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, and I will share more information about this revision in the second link below.

Linear Algebra Resources

  • Applied Linear Algebra and Matrix Analysis My textbook for an introductory linear algebra course, first edition, 2007.
  • Applied Linear Algebra and Matrix Analysis, 2nd Ed. My textbook for an introductory linear algebra course, revised edition, 2018 (coming soon).
  • Maple Notebooks Tutorial notebooks in Maple, some of which are the basis for linear algebra projects.
  • Mathematica Notebooks Tutorial notebooks in Mathematica, some of which are the basis for linear algebra projects (in old Mathematica .ma and new .nb formats.)
  • Linear Algebra Octave Files Program files for a Matlab-like program called Octave which I have found very useful in linear algebra. With a little tweaking, these will run under Matlab.
  • Text versions of projects Some text files, mostly in Latex.
  • Sample Syllabi Here are sample syllabi which I have used along with my text, together with class policy statements. Format is html.
  • Sample Exams Here are sample exams which I have used along with my text; they are all latex files, so instructors may massage them to suit their own needs.

Random Notes and FAQ

Here are some random notes about topics of interest, comments by users and answere 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 and Linux (this is my own platform). 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, so I think that instructors ought to give serious consideration to using it or something close, like Octave, in their applied linear algebra courses, to give their students an edge up on skills they need to acquire. I've written a lot of 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 various unices 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.