Sheldon Axler’s Linear Algebra Done Right (4th Edition) represents a significant departure from traditional methods by avoiding the use of determinants until the very end. Linear Algebra Done Right - Fourth Edition
: It emphasizes the deep relationship between linear transformations and matrices.
The fourth edition of Linear Algebra by Friedberg, Insel, and Spence is widely regarded as one of the most comprehensive and rigorous treatments of the subject for advanced undergraduates.
: Beyond standard topics like vector spaces and inner product spaces, this edition includes a specialized section on singular value decomposition and the pseudoinverse.