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

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]. [0] https://www.amazon.com/Linear-Algebra-Stephen-H-Friedberg-ebook/dp/B003YNXP7U/ref=sr_1_30?ie=UTF8&qid=1469389674&sr=8-30&keywords=linear+algebra https://www.amazon.com/Linear-Algebra-Stephen-H-Friedberg-eb... [1] https://www.amazon.com/Modern-Introduction-Linear-Algebra/dp/1439800405/ref=sr_1_7?ie=UTF8&qid=1469389844&sr=8-7&keywords=ricardo+henry https://www.amazon.com/Modern-Introduction-Linear-Algebra/dp... [2] https://www.amazon.com/Linear-Algebra-Mathematics-Robert-Messer/dp/0065017285/ref=sr_1_1?ie=UTF8&qid=1469390271&sr=8-1&keywords=linear+algebra+gateway https://www.amazon.com/Linear-Algebra-Mathematics-Robert-Mes... [3] https://www.amazon.com/Linear-Algebra-Introduction-Mathematics-Undergraduate/dp/0387940995/ref=sr_1_1?ie=UTF8&qid=1469390501&sr=8-1&keywords=linear+algebra+valenza https://www.amazon.com/Linear-Algebra-Introduction-Mathemati... [4] https://www.amazon.com/Coding-Matrix-Algebra-Applications-Computer/dp/0615880991/ref=sr_1_2?ie=UTF8&qid=1469390643&sr=8-2&keywords=linear+algebra https://www.amazon.com/Coding-Matrix-Algebra-Applications-Co... [5] https://www.amazon.com/Algebra-Through-Geometry-Undergraduate-Mathematics/dp/0387975861/ref=sr_1_1?ie=UTF8&qid=1469390814&sr=8-1&keywords=linear+algebra+geometry https://www.amazon.com/Algebra-Through-Geometry-Undergraduat... [6] https://www.amazon.com/Advanced-Linear-Algebra-Graduate-Mathematics/dp/0387728287/ref=sr_1_1?ie=UTF8&qid=1469390934&sr=8-1&keywords=linear+algebra+roman https://www.amazon.com/Advanced-Linear-Algebra-Graduate-Math...