Advanced Linear Algebra
3rd edition

For the third edition, the author has added a new chapter on associative algebras that includes the well known characterizations of the finite-dimensional division algebras over the real field (a theorem of Frobenius) and over a finite field (Wedderburn's theorem) ; polished and refined some arguments (such as the discussion of reflexivity, the rational canonical form, best approximations and the definitions of tensor products) ; upgraded some proofs that were originally done only for finite-dimensional/rank cases ; added new theorems, including the spectral mapping theorem ; and considerably expanded the reference section with over a hundred references to books on linear algebra.