Title says it all, are there also any specific online courses or books you would recommend for the prerequisites? Thanks

J. W. Tanner
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    not much. all modern books i am aware of introduce basic set theory and start from scratch. – Zest Jul 07 '20 at 06:15

4 Answers4


It depends on how abstract you want it to be. If it's just and introductory course without a ton of abstractions and proofs, then honestly not much is needed as a prereq, maybe some basic calculus. If you want an abstract and proof heavy course then maybe some groups, rings, and fields (these would be necessary for a high level linear algebra course), set theory, and most importantly how to do proofs would probably be necessary. All of that is covered in a college discrete mathematics or introduction to proofs course.

So it's really up to you.

Assuming you know at least calculus then these are some good resources for an introductory course:

Linear Algebra: a geometric approach by T Shiffin and M.R. Adams

The Essence of Linear Algebra by 3blue1brown

For an intermediary course in linear algebra (proof based and abstract but still undergraduate level):

Linear Algebra and its Applications, by Peter D. Lax,

Linear Algebra Done Right by Sheldon Axler

For a graduate level course in linear algebra (very proof based, very abstract):

Advanced Linear Algebra by Steven Roman


There is a nice book called Linear Algebra by A.R. Rao and P. Bhimasankaram for development of theory and for problem book and problem solving tricks you can see Linear algebra and linear models by R. B. Bapat but in in these book not cover the topic linear transformation approach and further reading I suggest the book Matrix Algebra From a Statistician's Perspective by David A. Harville this book contain huge ammount of topics.

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Basic arithmetic and set theory were the only prerequisites for the linear algebra that I learned in undergrad.

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To start you can read Stanley Grossman's linear algebra book, it is a basic book that allows you to understand some important concepts and has a number of good exercises and examples. Once you have studied this book, you can read Pita Ruíz's linear algebra book (it is in Spanish, I don't know if it has an English version) this book is of a higher level of difficulty than Stanley and very good.

Also, I suggest Gilbert Strang's text for linear algebra. That book is a treasure.

If you want to dig deeper into the topics, then the ideal is the linear algebra text by S. Friedberg A. Insel L. Spence. I still use the text as a reference for my classes.