文档介绍：Preface to the Third Edition
Let me begin by thanking the readers of the second edition for their many
ments 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
mapping theorem and a theorem to the effect that dim²= ³ dim ²=i 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
Preface to the Second Edition
Let me begin by thanking the readers of the first edition for their many helpful
comments and suggestions. The second edition represents a major change from
the first edition. Indeed, one might say that it is a totally new book, with the
exception of the general range of topics covered.
The text has pletely rewritten. I hope that an additional 12 years and
roughly 20 books worth of experience has enabled me to improve the quality of
my exposition. Also, the exercise sets have pletely rewritten.
The second edition contains two new chapters: a chapter on convexity,
separation and positive solutions to linear systems ( Chapter 15) and a chapter on
the QR position, singular values and pseudoinverses ( Chapter 17). The
treatments of tensor products and t