Page 7 - Advanced Linear Algebra

Preface to the Third Edition

Let me begin by thanking the readers of the second edition for their many
helpful comments and suggestions, with special thanks to Joe Kidd and Nam
Trang. For the third edition, I have corrected all known errors, polished and
refined some arguments (such as the discussion of reflexivity, the rational
canonical form, best approximations and the definitions of tensor products) and
upgraded some proofs that were originally done only for finite-dimensional/rank
cases. I have also moved some of the material on projection operators to an
earlier position in the text.

A few new theorems have been added in this edition, including the spectral
i
mapping theorem and a theorem to the effect that dim²= ³  dim²= ³ , with
equality if and only if is finite-dimensional.
=
I have also 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).
The reference section has been enlarged considerably, with over a hundred
references to books on linear algebra.

Steven Roman Irvine, California, May 2007