Most linear algebra texts have a wealth of information to impart, but courses are often challenged to find the time to get to the "good stuff," meaning inner product spaces and associated applications. Consequently, these crucial ideas often get short shrift.
Moreover, examples which are done in class are often too small to demonstrate effectively all facets of the theory, and time constraints limit the number of examples which can be done. However, computational software such as SageMath allow both the student and instructor to work more complex examples, hopefully providing a more nuanced understanding of the material.
Learning is an iterative process, enhanced by understanding examples and turning ideas over and over until they feel natural. It is hoped these materials begin to advance that mission. This page contains links to resources which will hopefully serve three different audiences:
Both the Linear Algebra Companion and Refresher were written using PreTeXt which allows for multiple formats to be generated from a single XML source. Salient features of the HTML versions below are: Live Sage computations and most links are generally presented as knowls. What the latter means is that when the text says "by Theorem 3.2" or "equation (4.1)", clicking the link with that reference displays the content in place, obviating the need to scroll back through the material to find the reference. Clicking again rolls the content back up. This convenience dramatically enhances the readability of the material.
Neither resource is intended as a textbook, though each summarizes topics and give examples, offering proofs when instructive. The understanding is that these resources have been preceded by course lectures, or in the case of the refresher, an entire course. In that context, these material provide a second pass through the material hopefully adding a layer of understanding.
Caveat: This project remains under development, and these resources are simply the current draft. Comments and suggestions are welcome, well some more than others.
Here is a link for the Sage Reference Manuals.