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Linear Algebra and Matrices: Topics for a Second Course
 
Helene Shapiro Swarthmore College, Swarthmore, PA
Front Cover for Linear Algebra and Matrices
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Hardcover ISBN: 978-1-4704-1852-6
Product Code: AMSTEXT/24
List Price: $72.00
MAA Member Price: $64.80
AMS Member Price: $57.60
Electronic ISBN: 978-1-4704-2272-1
Product Code: AMSTEXT/24.E
List Price: $67.00
MAA Member Price: $60.30
AMS Member Price: $53.60
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List Price: $108.00
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  • Front Cover for Linear Algebra and Matrices
  • Back Cover for Linear Algebra and Matrices
Linear Algebra and Matrices: Topics for a Second Course
Helene Shapiro Swarthmore College, Swarthmore, PA
Available Formats:
Hardcover ISBN:  978-1-4704-1852-6
Product Code:  AMSTEXT/24
List Price: $72.00
MAA Member Price: $64.80
AMS Member Price: $57.60
Electronic ISBN:  978-1-4704-2272-1
Product Code:  AMSTEXT/24.E
List Price: $67.00
MAA Member Price: $60.30
AMS Member Price: $53.60
Bundle Print and Electronic Formats and Save!
This product is available for purchase as a bundle. Purchasing as a bundle enables you to save on the electronic version.
List Price: $108.00
MAA Member Price: $97.20
AMS Member Price: $86.40
  • Book Details
     
     
    Pure and Applied Undergraduate Texts
    Volume: 242015; 317 pp
    MSC: 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 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.

  • 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
    • Error-correcting codes
    • Linear dynamical systems
    • Bibliography
    • Index
    • Other titles in this series
    • Back Cover
  • 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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Volume: 242015; 317 pp
MSC: 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 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.

  • 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
  • Error-correcting 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
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