Nonnegative Matrices And Applicable Topics In Linear Algebra
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Nonnegative Matrices and Applicable Topics in Linear Algebra
Author: Alexander Graham
language: en
Publisher: Courier Dover Publications
Release Date: 2019-11-13
Concise treatment covers graph theory, unitary and Hermitian matrices, and positive definite matrices as well as stochastic, genetic, and economic models. Problems, with solutions, enhance the text. 1987 edition.
Nonnegative Matrices and Applications
Author: R. B. Bapat
language: en
Publisher: Cambridge University Press
Release Date: 1997-03-28
This book provides an integrated treatment of the theory of nonnegative matrices (matrices with only positive numbers or zero as entries) and some related classes of positive matrices, concentrating on connections with game theory, combinatorics, inequalities, optimisation and mathematical economics. The wide variety of applications, which include price fixing, scheduling and the fair division problem, have been carefully chosen both for their elegant mathematical content and for their accessibility to students with minimal preparation. Many results in matrix theory are also presented. The treatment is rigorous and almost all results are proved completely. These results and applications will be of great interest to researchers in linear programming, statistics and operations research. The minimal prerequisites also make the book accessible to first-year graduate students.
Linear Algebra and Matrices
Author: Helene Shapiro
language: en
Publisher: American Mathematical Soc.
Release Date: 2015-10-08
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.