I just recently finally bought Strang's introduction to Linear Algebra. The book itself is very dense and, dare I say, scary to a newcomer, but his videos are amazingly clear in combination with the book.
I am in the beginning, but so far, I'd recommend the book. Though, the steep price (almost 100USD over here) makes it a bit difficult to recommend. I might buy Boyd’s and Vandenberghe’s Introduction to Applied Linear Algebra later and write a comparison.
Jim Hefferon, who is also a HN member, has a great free Linear Algebra textbook. People all have their own preferences but I actually prefer his to Strang's.
My sense is that Vandenberghe is great for getting your feet wet and building intuition, but it's not as deep as Strang in its coverage and has fewer problems. Definitely still worth reading through especially since the problems lend themselves well to working through with Julia or Python or similar.
For further reading, try Matrix Analysis and Applied Linear Algebra by Meyer.
I am in the beginning, but so far, I'd recommend the book. Though, the steep price (almost 100USD over here) makes it a bit difficult to recommend. I might buy Boyd’s and Vandenberghe’s Introduction to Applied Linear Algebra later and write a comparison.