**Pure and Applied Undergraduate Texts**

Volume: 45;
2020;
306 pp;
Softcover

MSC: Primary 15;

**Print ISBN: 978-1-4704-5670-2
Product Code: AMSTEXT/45**

List Price: $85.00

AMS Member Price: $68.00

MAA Member Price: $76.50

**Electronic ISBN: 978-1-4704-5918-5
Product Code: AMSTEXT/45.E**

List Price: $85.00

AMS Member Price: $68.00

MAA Member Price: $76.50

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#### Supplemental Materials

# Linear Algebra

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*Michael E. Taylor*

This text develops linear algebra with the view that it is an
important gateway connecting elementary mathematics to more advanced
subjects, such as advanced calculus, systems of differential
equations, differential geometry, and group representations. The
purpose of this book is to provide a treatment of this subject in
sufficient depth to prepare the reader to tackle such further
material.

The text starts with vector spaces, over the sets of real and
complex numbers, and linear transformations between such vector
spaces. Later on, this setting is extended to general fields. The
reader will be in a position to appreciate the early material on this
more general level with minimal effort.

Notable features of the text include a treatment of determinants,
which is cleaner than one often sees, and a high degree of contact
with geometry and analysis, particularly in the chapter on linear
algebra on inner product spaces. In addition to studying linear
algebra over general fields, the text has a chapter on linear algebra
over rings. There is also a chapter on special structures, such as
quaternions, Clifford algebras, and octonions.

#### Readership

Undergraduate and graduate students interested in linear algebra.

#### Table of Contents

# Table of Contents

## Linear Algebra

- Cover Cover11
- Title Page iii4
- Preface vii8
- Some basic notation xiii14
- Chapter 1. Vector spaces, linear transformations, and matrices 116
- Chapter 2. Eigenvalues, eigenvectors, and generalized eigenvectors 4762
- Chapter 3. Linear algebra on inner product spaces 7186
- 3.1. Inner products and norms 7388
- 3.2. Norm, trace, and adjoint of a linear transformation 8095
- 3.3. Self-adjoint and skew-adjoint transformations 85100
- 3.4. Unitary and orthogonal transformations 94109
- 3.5. Schurβs upper triangular representation 102117
- 3.6. Polar decomposition and singular value decomposition 106121
- 3.7. The matrix exponential 113128
- 3.8. The discrete Fourier transform 126141

- Chapter 4. Further basic concepts: duality, convexity, quotients, positivity 139154
- Chapter 5. Multilinear algebra 157172
- Chapter 6. Linear algebra over more general fields 175190
- Chapter 7. Rings and modules 189204
- Chapter 8. Special structures in linear algebra 231246
- Appendix A. Complementary results 277292
- Bibliography 301316
- Index 303318
- Selected Published Titles in This Series 307322
- Back Cover Back Cover1323