by Kenneth Hoffman and Ray Kunze
Linear Algebra is very well understood topic and there are tons of books about the subject. In my opinion in order to decide which book to follow one has to decide if he or she wants a more abstract treatment or a more concrete one with real-world applications (which are endless). Hoffman-Kunze’s book probably lays on the first kind of book. However, the first part of the book is a solid treatment of the first aspects of Linear Algebra, like linear systems and computation with matrices.