Linear Algebra has been part of the undergraduate mathematics curriculum for a long time. Since the subject is so widely applicable and useful, there are a great many introductions available. An Amazon or Google search for “linear algebra” will turn up too many items to keep in your head at once.
My favorite introductory text is our textbook: Introduction to Linear Algebra by Gilbert Strang, which is now it a fouth edition. In particular, I like Strang’s emphasis on the four fundamental subspaces and the Fundamental Theorem of Linear Algebra.
Prof Strang is on the faculty at MIT, and has made many of his materials available. I encourage you to look at these:
MIT OpenCourseWare Math 18.06: This is a complete semester of Strang’s course for which he wrote this text. A whole semester of video lectures is available.
Older MIT 18.06: This has more video, homework and solutions, review questions, etc… going back to 1996.
Strang’s Ideas Site to accompany the book
To run this class, I am writing (and constantly revising) a workbook to accompany Strang’s text. This is where you will find my commentary on the mathematics, some instruction on related Sage commands, and your daily homework tasks.
YouTube user 3Blue1Brown has a fantastic set of videos about core geometric ideas in linear algebra.
There is a bit of momentum building in a small corner of the mathematics community for creating and using open educational materials. There are two such books on linear algebra which you might find useful.
These books are written for courses pitched in different ways than ours, so it may not be obvious how to use them. But it can often help to have a different viewpoint to read, so I want to make you aware of these.
Rob Beezer has written a short and compact handout with the most useful linear algebra commands on it. You might want a copy to tuck in your book.
There are two reasonable references for the basics of SageMath (which are not the documentation):