Linear Algebra Textbooks


I was wondering whether anybody could please recommend a linear algebra textbook. I already have ‘Linear Algebra’ by Shilov but I opened the first page and it didn’t make any sense to me.

I know Rachel suggests some textbooks in Lecture 1. Would these be more accessible? Or should I be starting somewhere else and if so, where?

Grateful for any suggestions.


Introduction to Applied Linear Algebra by Boyd and Vandenberghe is pretty good.

Introduction to Linear Algebra by gilbert strang. His course he taught at MIT based on his book can be found on ocw by searching for 18.06 and picking the one he taught. Highly recommend.

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Thank you :slight_smile:

I will check both recommendations out.


I should also Mention that Gilbert Strang also has a “Learning From Data” textbook as well, with the course lectures on OCW as well. It’s an applied linear algebra book focused on machine learning/AI.

His lectures on both courses are well worth listening to in addition to the books.

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I’ve heard that Linear Algebra Done Right by Sheldon Axler is a good textbook.

I think this is a “love it or hate it” book. I have a copy and refer to it occasionally. It’s pretty informal and if you enjoy the writing style and if you click with Gilbert Strang’s wavelength of intuition then you may love it. I appreciate this book but I prefer others (see other posts).

One thing I love about this book is the focus it makes on understanding the essential spaces: column space, row space and null space. If you can understand these, the relationships between them, and develop some intuition for their geometric interpretations, then this is a solid foundation for all of linear algebra.

It’s an excellent second textbook, as the blurb on the back cover says. As a first textbook it’s a bit fussy.

One interesting thing between Axler and OP’s (@wildman’s) book (“Linear Algebra” by Shilov) is that Axler seems to regard determinants as a necessary evil and relegates the determinants chapter to the very end. Shilov, on the other hand, opens the book with a nice discussion in a chapter devoted to determinants right at the beginning.

The thing I love about this book is that it has a really great summary of all the important points in linear algebra. If you have already studied linear algebra and you want to apply it to machine learning then this might be an ideal book.

One of my favorite first books on linear algebra is “Elementary Linear Algebra” by Anton and Rorres. A solutions manual is also available. This book is at the level of a first year mathematics undergraduate student.

It’s good to get a solid grounding in both matrices (where linear transformations as represented by matrices depend on the basis) and pure linear algebra (where linear transformations are independent of their basis). I’ve indicated in parentheses the major differences between the systems. The matrix approach is also more immediately amenable to computation too. I think Anton & Rorres do a good job of explaining both the “matrix and applications” approach and the pure approach.

I browsed through an online copy and I was disappointed to see that it misses many fundamental linear algebra topics, e.g., nullspace. On the other hand as a course this book is great with the applications and gets you using LA in pattern classification problems very quickly for example. The work “Introduction” shouldn’t be in the title but I would still like to have this one on my bookshelf as a valued book that takes a very different perspective.