
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 HP28 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 SpringerVerlag 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
Matlablike 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.
 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.
 What's LyX and what does it have to do with
teaching? Glad you asked. This is a program that
notenoughpeople 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.
