Hardcover ISBN:  9781470418526 
Product Code:  AMSTEXT/24 
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Electronic ISBN:  9781470422721 
Product Code:  AMSTEXT/24.E 
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Book DetailsPure and Applied Undergraduate TextsVolume: 24; 2015; 317 ppMSC: Primary 15; 05;
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 betterknown 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.
ReadershipUndergraduate and graduate students and research mathematicians interested in linear algebra, linear systems, graph theory, block designs, matrices, and error correcting codes.

Table of Contents

Cover

Title page

Contents

Preface

Note to the reader

Preliminaries

Inner product spaces and orthogonality

Eigenvalues, eigenvectors, diagonalization, and triangularization

The Jordan and Weyr canonical forms

Unitary similarity and normal matrices

Hermitian matrices

Vector and matrix norms

Some matrix factorizations

Field of values

Simultaneous triangularization

Circulant and block cycle matrices

Matrices of zeros and ones

Block designs

Hadamard matrices

Graphs

Directed graphs

Nonnegative matrices

Errorcorrecting codes

Linear dynamical systems

Bibliography

Index

Other titles in this series

Back Cover


Additional Material

Reviews

"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


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

Cover

Title page

Contents

Preface

Note to the reader

Preliminaries

Inner product spaces and orthogonality

Eigenvalues, eigenvectors, diagonalization, and triangularization

The Jordan and Weyr canonical forms

Unitary similarity and normal matrices

Hermitian matrices

Vector and matrix norms

Some matrix factorizations

Field of values

Simultaneous triangularization

Circulant and block cycle matrices

Matrices of zeros and ones

Block designs

Hadamard matrices

Graphs

Directed graphs

Nonnegative matrices

Errorcorrecting codes

Linear dynamical systems

Bibliography

Index

Other titles in this series

Back Cover

"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