2008;
371 pp;
Hardcover

MSC: Primary 15;
Secondary 34; 35; 39; 42

**Print ISBN: 978-0-8218-4441-0
Product Code: MBK/50**

List Price: $69.00

AMS Member Price: $55.20

MAA Member Price: $62.10

**Electronic ISBN: 978-1-4704-1200-5
Product Code: MBK/50.E**

List Price: $65.00

AMS Member Price: $52.00

MAA Member Price: $58.50

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#### Supplemental Materials

# Applied Linear Algebra: The Decoupling Principle, Second Edition

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*Lorenzo Sadun*

Linear algebra permeates mathematics, as well as physics and
engineering. In this text for junior and senior undergraduates, Sadun
treats diagonalization as a central tool in solving complicated problems
in these subjects by reducing coupled linear evolution problems to a
sequence of simpler decoupled problems. This is the Decoupling
Principle.

Traditionally, difference equations, Markov chains, coupled oscillators,
Fourier series, the wave equation, the Schrödinger equation, and
Fourier transforms are treated separately, often in different courses.
Here, they are treated as particular instances of the decoupling
principle, and their solutions are remarkably similar. By understanding
this general principle and the many applications given in the book,
students will be able to recognize it and to apply it in many other
settings.

Sadun includes some topics relating to infinite-dimensional spaces. He
does not present a general theory, but enough so as to apply the
decoupling principle to the wave equation, leading to Fourier series and
the Fourier transform.

The second edition contains a series of Explorations. Most are
numerical labs in which the reader is asked to use standard computer
software to look deeper into the subject. Some explorations are
theoretical, for instance, relating linear algebra to quantum
mechanics. There is also an appendix reviewing basic matrix operations
and another with solutions to a third of the exercises.

#### Readership

Undergraduate students interested in linear algebra; applications of linear algebra.

#### Reviews & Endorsements

Sadun's writing style [is] very natural and straightforward. The book has a large number of exercises, ranging from the computational to the theoretical. ...For all these reasons, I can imagine using Sadun's books in a number of different ways. The author's exposition is so clear and littered with examples and motivation for the material that I would not hesitate to point a student wishing to do an independent study to this book. If we were to teach a second semester of linear algebra, I would certainly consider this book to be a frontrunner as a choice of texts. As it is, I will keep this book on my desk next time I teach our existing linear algebra course, as a source of examples, problems, and ideas for my own teaching.

-- MAA Reviews

This is a book which can be recommended to anyone interested in the mathematical foundation of principles and techniques used in many applications of Linear Algebra to the real world.

-- Monatshafte für Mathematik

# Table of Contents

## Applied Linear Algebra: The Decoupling Principle, Second Edition

- Cover Cover11
- Title page i2
- Dedication page iii4
- Contents v6
- Preface to second edition ix10
- Preface xi12
- The decoupling principle 120
- Vector spaces and bases 928
- Linear transformations and operators 3756
- An introduction to eigenvalues 5776
- Some crucial applications 97116
- Inner products 145164
- Adjoints, Hermitian operators, and unitary operators 189208
- The wave equation 223242
- Continuous spectra and the Dirac delta function 259278
- Fourier transforms 281300
- Green’s functions 311330
- Matrix operations 337356
- Solutions to selected exercises 345364
- Index 369388
- Back Cover Back Coveri394