Page 8 - A Course in Linear Algebra with Applications

PREFACE TO THE SECOND EDITION

The principal change from the first edition is the addition of
a new chapter on linear programming. While linear program-
ming is one of the most widely used and successful applications
of linear algebra, it rarely appears in a text such as this. In
the new Chapter Ten the theoretical basis of the simplex algo-
rithm is carefully explained and its geometrical interpretation
is stressed.
Some further applications of linear algebra have been
added, for example the use of Jordan normal form to solve
systems of linear differential equations and a discussion of ex-
tremal values of quadratic forms.
On the theoretical side, the concepts of coset and quotient
space are thoroughly explained in Chapter 5. Cosets have
useful interpretations as solutions sets of systems of linear
equations. In addition the Isomorphisms Theorems for vector
spaces are developed in Chapter Six: these shed light on the
relationship between subspaces and quotient spaces.
The opportunity has also been taken to add further exer-
cises, revise the exposition in several places and correct a few
errors. Hopefully these improvements will increase the use-
fulness of the book to anyone who needs to have a thorough
knowledge of linear algebra and its applications.
I am grateful to Ms. Tan Rok Ting of World Scientific
for assistance with the production of this new edition and for
patience in the face of missed deadlines. I thank my family
for their support during the preparation of the manuscript.

Derek Robinson
Urbana, Illinois
May 2006

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