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 beauty of these subjects as
well as the mechanics. To this end, applied mathematics and mathematical
modeling ought to have an important role in an introductory treatment of
linear algebra. In this way students see that concepts of matrix and linear
algebra make concrete problems workable.
In this book we weave significant motivating examples into the fabric of
the text. I hope that instructors will not omit this material; that would be
a missed opportunity for linear algebra! The text has a strong orientation
toward numerical computation and applied mathematics, which means that
matrix analysis plays a central role. All three of the basic components of lin-
ear algebra — theory, computation, and applications — receive their due.
The proper balance of these components gives 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 experimental science; this emphasis is
found in certain examples, computer exercises, and projects. Contemporary
mathematical software make ideal “labs” for mathematical experimentation.
Nonetheless, this text is independent of specific hardware and software plat-
forms. Applications and ideas should take center stage, not software.
This book is designed for an introductory course in matrix and linear
algebra. Here are some of its main goals:
• To provide a balanced blend of applications, theory, and computation that
emphasizes their interdependence.
• To assist those who wish to incorporate mathematical experimentation
through computer technology into the class. Each chapter has computer
exercises sprinkled throughout and an optional section on computational
notes. Students should use the locally available tools to carry out the experiments suggested in the project and use the word processing capabilities
of their computer system to create reports of results.
To help students to express their thoughts clearly. Requiring written re-
ports is one vehicle for teaching good expression of mathematical ideas.
To encourage cooperative learning. Mathematics educators are becoming
increasingly appreciative of this powerful mode of learning. Team projects
and reports are excellent vehicles for cooperative learning.
To promote individual learning by providing a complete and readable text.
I hope that readers will find the text worthy of being a permanent part of
their reference library, particularly for the basic linear algebra needed in
the applied mathematical sciences.