Besides, books have different levels and audiences. I learned Linear Algebra from three books:
1) Gilbert Strang's "Introduction to Linear Algebra" was great because Gilbert goes straight to intuitions, the proofs are simple, most exercises have answers, but it does not cover advanced material. I used this book for self-teaching. You could probably learn from it with just high-school level maths. Good for engineers.
2) Hoffman and Kunze's "Linear Algebra" was given as a textbook for my first LA course. While it covered some topics that weren't found in many other textbooks and are not really "standard curricula" in many other universities for (jordan normal form, rational canonical form). I found it more similar to a reference than a textbook; it is intended for math majors. The proofs are imho a bit obtuse and it usually introduces topics without much justification. Determinants are introduced early.
3) Axler's "Linear Algebra Done Right" OTOH covered many of the topics in Hoffman&Kunze but the organization and the proofs were (imho) mucho more clear and motivated. Also intended for math majors. No determinants until the end.
1) Gilbert Strang's "Introduction to Linear Algebra" was great because Gilbert goes straight to intuitions, the proofs are simple, most exercises have answers, but it does not cover advanced material. I used this book for self-teaching. You could probably learn from it with just high-school level maths. Good for engineers.
2) Hoffman and Kunze's "Linear Algebra" was given as a textbook for my first LA course. While it covered some topics that weren't found in many other textbooks and are not really "standard curricula" in many other universities for (jordan normal form, rational canonical form). I found it more similar to a reference than a textbook; it is intended for math majors. The proofs are imho a bit obtuse and it usually introduces topics without much justification. Determinants are introduced early.
3) Axler's "Linear Algebra Done Right" OTOH covered many of the topics in Hoffman&Kunze but the organization and the proofs were (imho) mucho more clear and motivated. Also intended for math majors. No determinants until the end.