The Axler text was discussed here (631 pts 295 comments):

https://news.ycombinator.com/item?id=38060159

For most people going into science and engineering as opposed to pure mathematics, Poole's "Linear Algebra: A Modern Introduction" is probably more suitable as it's heavy on applications, such as Markov chains, error-correcting codes, spatiel orientation in robotics, GPS calculations, etc.

https://www.physicsforums.com/threads/linear-algebra-a-moder...