Preface
This book is about matrix and linear algebra, and their applications. For many students
the tools of matrix and linear algebra will be as fundamental in their professional work
as the tools of calculus; thus it is important to ensure that students appreciate the utility
and beautyof these subjects, as well as understand the mechanics. One way to do so is to
show how concepts of matrix and linear algebra make concrete problems workable. To
this end, applied mathematics and mathematical modeling ought to have an important
role in an introductory treatment of linear algebra.
One of the features of this book is that we weave significant motivating examples into
the fabric of the text. Needless to say, I hope that instructors will not omit this ma-
terial; that would be a missed opportunity for linear algebra! The text has a strong
orientation towards numerical computation and applied mathematics, which means that
matrix analysis plays a central role. All three of the basic components of linear algebra
– theory, computation and applications – receive their due. The proper balance of these
components will give a diverse audience of physical science, social science, statistics,
engineering and math students the tools they need as well as the motivation to acquire
these tools. Another feature of this text is an emphasis on linear algebra as an exper-
imental science; this emphasis is to be found in certain examples, computer exercises
and projects. Contemporary mathematical software makes an ideal “lab” for mathemat-
ical experimentation. At the same time, this text is independent of specific hardware
and software platforms. Applications and ideas should play center stage, not software.
This book is designed for an introductory course in matrix and linear algebra. It is
assumed that the student has had some exposure to calculus. Here are some of its main
goals:
To provide a balanced blend of applications, theory and computation which em-
phasizes their interdependence.
To assist those who wish to incorporate mathematical experimentation through
computer technology into the class. Each chapter has an optional section on
computational notes and projects and computer exercises sprinkled throughout.
The student should use the locally available tools to carry out the experiments
suggested in the project and use the word processing capabilities of the com-
puter system to create small reports on his/her results. In this way they gain
experience in the use of the computer as a mathematical tool. One can also en-
vision reports on a grander scale as mathematical “term papers.” I have made
such assignments in some of my own classes with delightful results. A few
major report topics are included in the text.
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