**Pure and Applied Undergraduate Texts**

Volume: 24;
2015;
317 pp;
Hardcover

MSC: Primary 15; 05;

**Print ISBN: 978-1-4704-1852-6
Product Code: AMSTEXT/24**

List Price: $72.00

AMS Member Price: $57.60

MAA Member Price: $64.80

**Electronic ISBN: 978-1-4704-2272-1
Product Code: AMSTEXT/24.E**

List Price: $67.00

AMS Member Price: $53.60

MAA Member Price: $60.30

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#### Supplemental Materials

# Linear Algebra and Matrices: Topics for a Second Course

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*Helene Shapiro*

Linear algebra and matrix theory are fundamental tools for almost every area of mathematics, both pure and applied. This book combines coverage of core topics with an introduction to some areas in which linear algebra plays a key role, for example, block designs, directed graphs, error correcting codes, and linear dynamical systems. Notable features include a discussion of the Weyr characteristic and Weyr canonical forms, and their relationship to the better-known Jordan canonical form; the use of block cyclic matrices and directed graphs to prove Frobenius's theorem on the structure of the eigenvalues of a nonnegative, irreducible matrix; and the inclusion of such combinatorial topics as BIBDs, Hadamard matrices, and strongly regular graphs. Also included are McCoy's theorem about matrices with property P, the Bruck–Ryser–Chowla theorem on the existence of block designs, and an introduction to Markov chains. This book is intended for those who are familiar with the linear algebra covered in a typical first course and are interested in learning more advanced results.

#### Readership

Undergraduate and graduate students and research mathematicians interested in linear algebra, linear systems, graph theory, block designs, matrices, and error correcting codes.

#### Reviews & Endorsements

"Linear Algebra and Matrices: Topics for a Second Course" by Helene Shapiro succeeds brilliantly at its slated purpose which is hinted at by its title. It provides some innovative new ideas of what to cover in the second linear algebra course that is offered at many universities...[this book] would be my personal choice for a textbook when I next teach the second course for linear algebra at my university. I highly recommend this book, not only for use as a textbook, but also as a source of new ideas for what should be in the syllabus of the second course.

-- Rajesh Pereira, IMAGE

#### Table of Contents

# Table of Contents

## Linear Algebra and Matrices: Topics for a Second Course

- Cover Cover11 free
- Title page iii4 free
- Contents v6 free
- Preface xi12 free
- Note to the reader xv16 free
- Preliminaries 118 free
- Inner product spaces and orthogonality 1734
- Eigenvalues, eigenvectors, diagonalization, and triangularization 3956
- The Jordan and Weyr canonical forms 5168
- Unitary similarity and normal matrices 7794
- Hermitian matrices 89106
- Vector and matrix norms 113130
- Some matrix factorizations 121138
- Field of values 143160
- Simultaneous triangularization 151168
- Circulant and block cycle matrices 163180
- Matrices of zeros and ones 169186
- Block designs 185202
- Hadamard matrices 207224
- Graphs 221238
- Directed graphs 235252
- Nonnegative matrices 249266
- Error-correcting codes 265282
- Linear dynamical systems 279296
- Bibliography 303320
- Index 311328 free
- Other titles in this series 319336
- Back Cover Back Cover1338