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 considerably expanded the reference section with over a hundred
references to books on linear algebra. From the reviews of the second edition: "In this 2nd
edition the author has rewritten the entire book and has added more than 100 pages of new
materials....As in the previous edition the text is well written and gives a thorough
discussion of many topics of linear algebra and related fields...the exercises are rewritten
and expanded....Overall I found the book a very useful one....It is a suitable choice as a
graduate text or as a reference book." Ali-Akbar Jafarian ZentralblattMATH "This is a
formidable volume a compendium of linear algebra theory classical and modern... The
development of the subject is elegant...The proofs are neat...The exercise sets are good with
occasional hints given for the solution of trickier problems...It represents linear algebra and
does so comprehensively." Henry Ricardo MAA Online
