My favorite LA books are Linear Algebra by Friedberg/Insel[0] which is a combination of Axler style book with more computation oriented one (Terry Tao has a set of lectures based off this book). Another one I like is Modern Intro To LA by Henry Ricardo[1] which implicitly introduced me to Replacement theorem which is really overlooked in a ton of LA books. Again, this book's a rigorous mixture of both theory and computation done very well. If you've never seen higher level math before, there's Linear Algebra: Gateway to Mathematics by Robert Messer[2]. It has tons of commentary about elementary set theory and proof techniques along the way. Whenever someone mentions Axler's book, someone else brings up Treil's book. But there's a third one in the same league/group which is Linear Algebra: An Introduction to Abstract Mathematics by Robert Valenza[3]. Other favorites are Coding the Matrix by Philip Klein[4] for Python aficionados and
Linear Algebra Through Geometry by Banchoff/Wermer[5] for those who like geometry.

If you are way beyond all this, you can still pick up new things from Advanced Linear Algebra by Steven Roman[6].

If you are way beyond all this, you can still pick up new things from Advanced Linear Algebra by Steven Roman[6].

[0] https://www.amazon.com/Linear-Algebra-Stephen-H-Friedberg-eb...

[1] https://www.amazon.com/Modern-Introduction-Linear-Algebra/dp...

[2] https://www.amazon.com/Linear-Algebra-Mathematics-Robert-Mes...

[3] https://www.amazon.com/Linear-Algebra-Introduction-Mathemati...

[4] https://www.amazon.com/Coding-Matrix-Algebra-Applications-Co...

[5] https://www.amazon.com/Algebra-Through-Geometry-Undergraduat...

[6] https://www.amazon.com/Advanced-Linear-Algebra-Graduate-Math...