How should I approach the study of Linear Algebra?

Here are some suggestions that may help.

$\bullet$ How to self study Linear Algebra. See my response and the other responses.

Study Habits from Math Stack Exchange

$\bullet$ What are some good math study habits?

$\bullet$ How to study math to really understand it and have a healthy lifestyle with free time?

$\bullet$ How can I learn to read maths at a University level?

Free Resources

$\bullet$ MIT Open Course Ware. You can also find others at other universities and these have free course notes and video lectures.

$\bullet$ Khan Academy.

$\bullet$ Wiki Books Linear Algebra Resources

$\bullet$ Linear Algebra for Communications: A gentle introduction. I would study this to give you context!

$\bullet$ College Libraries: Peruse the books in the library and see if any fit the style you like.

Book Recommendations

$\bullet$ Linear Algebra Through Geometry, Thomas Banchoff, John Wermer (since you are visual)

$\bullet$ Practical Linear Algebra: A Geometry Toolbox, Gerald Farin, Dianne Hansford (since you are visual)

$\bullet$ Linear Algebra Done Right, Sheldon Axler

$\bullet$ Linear Algebra and Its Applications, David C. Lay

$\bullet$ Linear Algebra Textbook Recommendations on MSE

$\bullet$ Alternative to Axler's “Linear Algebra Done Right”

Problem Books

It is very helpful to do problems and practice, practice, practice to reinforce concepts!

$\bullet$ Linear Algebra Problem Book, Paul R. Halmos

$\bullet$ The Linear Algebra a Beginning Graduate Student Ought to Know, Jonathan Golan.

$\bullet$ 3,000 Solved Problems in Linear Algebra, Seymour Lipschutz

$\bullet$ Schaum's Outline of Linear Algebra Fourth Edition, Seymour Lipschutz, Marc Lipson

History of Linear Algebra

Linear Algebra History Websites

Regards

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