A First Course in Linear Algebra

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Embedded Sage Cells

(2013/08/17): FCLA is the first textbook to have powerful mathematics software embedded directly in the text. Read below about Sage, and then head directly to the online edition of the book (ignoring the materials below, which are now very obsolete). The 95 vignettes about Sage each have a series of cells powered by the Sage Cell Server, so the complete computational power of the leading open source software for mathematics is at your fingertips as you learn linear algebra.

Sage Mathematics Software

Sage is an open-source program for doing mathematics and is the ideal companion to A First Course in Linear Algebra. Sage is designed to be a free, open-source alternative to Magma, Maple, Mathematica and Matlab. It includes many mature and powerful open-source tools for mathematics, including several devoted to linear algebra, with the result that exact linear algebra is one of Sage's strengths.

Sage-Enhanced Textbook

As part of a sabbatical project, I have contributed code to Sage for the purpose of making it even easier for a student to use productively. Allied with that project I have written 95 short introductions to various Sage commands and techniques. These alone are available as a PDF file below, organized according to the chapters of the book, and this material will soon be incorporated into the production versions of the text.

I have also created a new version of the entire book, available as a sequence of Sage worksheets. By using any Sage server, such as the freely available one at sagenb.org, or locally on your own computer, the text is readable in your web browser along with live, executable, editable Sage code and all the conveniences of the Sage notebook.

Preview Release (2011/08/03)

Compatible with FCLA Version 2.22, Sage Version 4.7.1


  1. Worksheet version is a collection of worksheets in one big zip file, which you must first download to your computer. Do not unzip the file. (If Safari unzips the file, look in the trash for the original, or configure Safari to not open "safe" files automatically.) Use the Sage notebook "Upload" function and provide the location of the zip file - the notebook will unzip the file into the worksheets that are sections of the book.
  2. Sections of the book will be placed in your list of worksheets ordered by the time they were created, so you may have to scroll down a ways to find them.
  3. Links within a worksheet are functional. But across worksheets they do not work since the Sage notebook does not yet support this. In particular, do not use Tables of Contents, just go straight to the desired section.
  4. New content runs just through the middle of Chapter R, which was always the original goal. Maybe someday there will be more added.
  5. There are a few font "issues" in Safari, like especially "swoopy" calligraphic characters.
  6. The text uses some Sage commands that are not in the official release of Sage. This should improve with time. See the Sage Wiki project page for current status.
  7. Please let me know if anything else is behaving strangely.

Sage Linear Algebra Tutorial

This is a presentation I gave at Sage Days 15, May 2009, intended as a quick introduction to the linear algebra capabilities of Sage. The video is about 45 minutes long, and should play in the embedded Flash viewer visible just below. You can download the sws file to view in the Sage Notebook if you would like to play along, or if you don't have Sage available, there is a PDF version you can page through. Finally, the "quick reference" sheet is a two-page summary of the core of Sage's linear algebra routines that was prepared in conjunction with this presentation.