Tried to pick a book to get into linear algebra recently, the experience was fairly hellish. First course this, second course that, done right, done wrong... I'd to the LADR4e route, but I don't have the proof-it chops yet...

I like Serge Lang's books for clarity of explanations. He has an Introduction to Linear Algebra which concisely covers the basics (265 pages in the main text), and grounds the matrix computations in the geometric interpretation.

Be aware that Lang has another book, called just "Linear Algebra", which is more theoretical.

You might want to checkout the book Practical Linear Algebra: A Geometry Toolbox by Dianne Hansford and Gerald Farin (its 1st edition was simply named The Geometry Toolbox: For Graphics and Modeling) to get an intuitive and visual introduction to Linear Algebra.

Pair it with Edgar Goodaire's Linear Algebra: Pure & Applied and you can transition nicely from intuitive geometric to pure mathematical approach. The author's writing style is quite accessible.

Add in Introduction to Applied Linear Algebra: Vectors, Matrices, and Least Squares by Stephen Boyd et al. and you are golden. Free book available at https://web.stanford.edu/~boyd/vmls/

I found the book "Linear Algebra" and accompanying lecture recordings by Jim Hefferon very approachable and solid.

It's free, including exercises and an (also free) solutions book.

I had the same experience when I first learned linear algebra. I don't have any book recommendations, but I did want to say that for some topics, it is better to learn it by applying it than by using a book. Linear algebra was like that for me, but oddly enough I was able to learn tensor calculus from a book later (after doing a lot of problems).

Thanks to everyone recommending books too!

I've found the "No bullshit Guide to Linear Algebra" pretty good. Could be worth checking it out. It's the one resource that has things click more for me.