A First Course in Linear Algebra

The linear algebra textbook with freedom

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Online

This is the online XML/MathML version of the free textbook "A First Course in Linear Algebra." If this is your first visit to this page, please read the material below about your choice of browsers and the likely need to install additional fonts. Otherwise, if you a returning visitor, click on through to the table of contents with the link immediately below. Previous versions are archived at the bottom of this page.

Latest Online Version - Table of Contents

Local Viewing

You can also obtain an archive with all the XML files if you wish to store them locally and view them without using a network connection. Check back often for updated versions. These are available on the download page.

Print vs. Online

This book has been conceived and designed to be printed and used as a physical book. Yes, very old-fashioned, I know. This means that it has been written with a PDF format in mind. However, even with the PDF format, reading the book on the screen can be very useful for learning the material since references to previous definitions and theorems are all hypertext links and it is easy to pop back and forth as you study a proof or example. Here we have converted our TeX sources into the MathML dialect of XML using Eitan Gurari's wonderful TeX4ht translator. This effort was not without a few hurdles, and Eitan was very helpful getting me over the final obstacles. After a few weeks of off-and-on effort fine-tuning the conversion and my TeX macros, it is now routine to automate the conversion and have an online version that is current with the latest revisions.

Displaying mathematics on web pages is an old problem, often accomplished by making many small images of the more involved typographic sections. These pages do not go that route. You will need a browser capable of interpreting MathML and you will need the broad range of fonts that mathematics demands. Here's what you need to know.

Browsers and Fonts

TeX4ht has a few switches to create output favorable to Mozilla's Firefox browser, and we have found this gives us the best output with the fewest compromises. Grab yourself a copy of Firefox if you don't have it already. Highly recommended, and free. Be sure to read the notes below about installing fonts. Here are browser-specific observations and cautions. Following that is a short, diminishing, list of rough spots that need work.

Firefox: These pages render amazingly well in Firefox straight out of the box. So if you are just stopping by casually, give them a view in Firefox. Square roots will be messed up, and some symbols, like angle brackets might be missing. Brackets for matrices and vectors may not be full-size. You will probably be prompted to add in some fonts when you first visit a page with mathematics on it, and long-run you will want to do that. Visit the information on installing fonts for usable instructions on getting the necessary fonts installed (they are free).

Internet Explorer: Out of the box, IE will choke on the first little bit of these files, so even for a casual visit you will have to take some extra steps. The solution is to download and install the MathPlayer plugin (its free), which appears to be an ActiveX control, which you may have to explicitly permit to run. I have one preliminary report from an experienced MathPlayer user that this works well with the pages here. However, links within displayed mathematics are not live in IE, and this is one of the best features of the PDF versions and the Firefox browser.

Amaya: Amaya is the World Wide Web Consortium's (W3C) testbed browser. Links to theorems and definitions from within math displays render just fine in this browser. There are still quite a few "issues" in other places, though, so I wouldn't recommend this over Firefox. I've tested briefly with version 9.52 for Windows. Download from http://www.w3.org/Amaya/

Opera: Opera seems to digest these files OK, but 2-D structures (like matrices) are not rendered correctly. Any insight into the combination of Opera and MathML would be appreciated.

Rough Spots

As of 2006/11/21, this is the short list of things that need fixing, beginning with the most likely to go away first. Eventually this list will go away entirely.
  1. Notation list needs fixes to load properly in Firefox. Loads in IE but has a few problems. Will likely fix soon.
  2. Commutative diagrams are now being created as graphics files, which are not coming into TeX4ht very well. See the PDF versions if you need to look at them.
  3. Some calligraphic letters for subspace constructions aren't always as stylish when viewed in Firefox. Compare a null space with a row space. If you need to know the reason, Firefox does not seem as keen to handle the Plane 1 Unicode fonts. IE seems to do much better with these.
  4. In Internet Explorer 6 with MathPlayer, links to previous theorems that are alongside displayed mathematics, will not work. This is one of the best features of the PDF versions, and will work well in Firefox.

Previous Versions

http://linear.ups.edu/online.html