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OverviewLinear 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. Full Product DetailsAuthor: Helene ShapiroPublisher: American Mathematical Society Imprint: American Mathematical Society Volume: 24 Weight: 0.740kg ISBN: 9781470418526ISBN 10: 1470418525 Pages: 318 Publication Date: 30 October 2015 Audience: Professional and scholarly , Professional & Vocational Format: Hardback Publisher's Status: Active Availability: In Print  This item will be ordered in for you from one of our suppliers. Upon receipt, we will promptly dispatch it out to you. For in store availability, please contact us. Table of Contents* 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* IndexReviews"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" 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 Author InformationHelene Shapiro, Swarthmore College, PA, USA. Tab Content 6Author Website:Countries AvailableAll regions |
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