Hallmark Features
Relationships Between Concepts One of the important goals of a course in linear algebra is to establish the intricate
thread of relationships between systems of linear equations, matrices, determinants, vectors, linear transformations, and
eigenvalues. That thread of relationships is developed through the following crescendo of theorems that link each new
idea with ideas that preceded it: 1.5.3, 1.6.4, 2.3.6, 4.3.4, 5.6.9, 6.2.7, 6.4.5, 7.1.5. These theorems bring a coherence to
the linear algebra landscape and also serve as a constant source of review.
Smooth Transition to Abstraction The transition from to general vector spaces is often difficult for students. To
smooth out that transition, the underlying geometry of is emphasized and key ideas are developed in before
proceeding to general vector spaces.
Early Exposure to Linear Transformations and Eigenvalues To ensure that the material on linear transformations
and eigenvalues does not get lost at the end of the course, some of the basic concepts relating to those topics are
developed early in the text and then reviewed and expanded on when the topic is treated in more depth later in the text.
For example, characteristic equations are discussed briefly in the chapter on determinants, and linear transformations from
to are discussed immediately after is introduced, then reviewed later in the context of general linear
transformations.
About the Exercises
Each section exercise set begins with routine drill problems, progresses to problems with more substance, and concludes with
theoretical problems. In most sections, the main part of the exercise set is followed by the Discussion and Discovery problems
described above. Most chapters end with a set of supplementary exercises that tend to be more challenging and force the
student to draw on ideas from the entire chapter rather than a specific section. The technology exercises follow the
supplementary exercises and are classified according to the section in which we suggest that they be assigned. Data for these
exercises in
MATLAB, Maple, and Mathematica formats can be downloaded from www.wiley.com/college/anton.
About Chapter 11
This chapter consists of 21 applications of linear algebra. With one clearly marked exception, each application is in its own
independent section, so that sections can be deleted or permuted freely to fit individual needs and interests. Each topic begins
with a list of linear algebra prerequisites so that a reader can tell in advance if he or she has sufficient background to read the
section.
Because the topics vary considerably in difficulty, we have included a subjective rating of each topic—easy, moderate, more
difficult. (See “A Guide for the Instructor” following this preface.) Our evaluation is based more on the intrinsic difficulty of
the material rather than the number of prerequisites; thus, a topic requiring fewer mathematical prerequisites may be rated
harder than one requiring more prerequisites.
Because our primary objective is to present applications of linear algebra, proofs are often omitted. We assume that the reader
has met the linear algebra prerequisites and whenever results from other fields are needed, they are stated precisely (with
motivation where possible), but usually without proof.
Since there is more material in this book than can be covered in a one-semester or one-quarter course, the instructor will have
to make a selection of topics. Help in making this selection is provided in the Guide for the Instructor below.
Supplementary Materials for Students
Student Solutions Manual, Ninth Edition—This supplement provides detailed solutions to most theoretical exercises and to at
least one nonroutine exercise of every type. (ISBN 0-471-43329-2)
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