Charles R. Johnson's Books

Matrix Theory and Applications

By: Charles R. Johnson

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Matrix Theory and Applications

By: Charles R. Johnson

This volume contains the lecture notes prepared for the AMS Short Course on Matrix Theory and Applications, held in Phoenix in January, 1989. Matrix theory continues to enjoy a renaissance that has accelerated in the past decade, in part because of stimulation from a variety of applications and considerable interplay with other parts of mathematics. In addition, the great increase in the number and vitality of specialists in the field has dispelled the popular misconception that the subject has been fully researched.

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Page Count

272

Publisher

American Mathematical Soc.

Published Date

ISBN 10

0821801546

ISBN 13

9780821801543

Topics in Matrix Analysis

By: Roger A. Horn,Charles R. Johnson

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Topics in Matrix Analysis

By: Roger A. Horn,Charles R. Johnson

This book treats several topics in matrix theory not included in its predecessor volume, Matrix Analysis.

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Page Count

620

Publisher

Cambridge University Press

Published Date

ISBN 10

0521467136

ISBN 13

9780521467131

Matrix Positivity

By: Charles R. Johnson,Ronald L. Smith,Michael J. Tsatsomeros

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Matrix Positivity

By: Charles R. Johnson,Ronald L. Smith,Michael J. Tsatsomeros

This comprehensive reference, for mathematical, engineering and social scientists, covers matrix positivity classes and their applications.

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Page Count

223

Publisher

Cambridge University Press

Published Date

ISBN 10

1108478719

ISBN 13

9781108478717

Matrix Analysis

By: Roger A. Horn,Charles R. Johnson

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Matrix Analysis

By: Roger A. Horn,Charles R. Johnson

Linear algebra and matrix theory are fundamental tools in mathematical and physical science, as well as fertile fields for research. This second edition of this acclaimed text presents results of both classic and recent matrix analysis using canonical forms as a unifying theme and demonstrates their importance in a variety of applications. This thoroughly revised and updated second edition is a text for a second course on linear algebra and has more than 1,100 problems and exercises, new sections on the singular value and CS decompositions and the Weyr canonical form, expanded treatments of inverse problems and of block matrices, and much more.

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Page Count

663

Publisher

Cambridge University Press

Published Date

ISBN 10

1139788884

ISBN 13

9781139788885

Eigenvalues, Multiplicities and Graphs

By: Charles R. Johnson,Carlos M. Saiago

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Eigenvalues, Multiplicities and Graphs

By: Charles R. Johnson,Carlos M. Saiago

The arrangement of nonzero entries of a matrix, described by the graph of the matrix, limits the possible geometric multiplicities of the eigenvalues, which are far more limited by this information than algebraic multiplicities or the numerical values of the eigenvalues. This book gives a unified development of how the graph of a symmetric matrix influences the possible multiplicities of its eigenvalues. While the theory is richest in cases where the graph is a tree, work on eigenvalues, multiplicities and graphs has provided the opportunity to identify which ideas have analogs for non-trees, and those for which trees are essential. It gathers and organizes the fundamental ideas to allow students and researchers to easily access and investigate the many interesting questions in the subject.

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Page Count

316

Publisher

Cambridge University Press

Published Date

ISBN 10

110854813X

ISBN 13

9781108548137

Totally Nonnegative Matrices

By: Shaun M. Fallat,Charles R. Johnson

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Totally Nonnegative Matrices

By: Shaun M. Fallat,Charles R. Johnson

Totally nonnegative matrices arise in a remarkable variety of mathematical applications. This book is a comprehensive and self-contained study of the essential theory of totally nonnegative matrices, defined by the nonnegativity of all subdeterminants. It explores methodological background, historical highlights of key ideas, and specialized topics. The book uses classical and ad hoc tools, but a unifying theme is the elementary bidiagonal factorization, which has emerged as the single most important tool for this particular class of matrices. Recent work has shown that bidiagonal factorizations may be viewed in a succinct combinatorial way, leading to many deep insights. Despite slow development, bidiagonal factorizations, along with determinants, now provide the dominant methodology for understanding total nonnegativity. The remainder of the book treats important topics, such as recognition of totally nonnegative or totally positive matrices, variation diminution, spectral properties, determinantal inequalities, Hadamard products, and completion problems associated with totally nonnegative or totally positive matrices. The book also contains sample applications, an up-to-date bibliography, a glossary of all symbols used, an index, and related references.

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Page Count

264

Publisher

Princeton University Press

Published Date

ISBN 10

0691242410

ISBN 13

9780691242415

Putting Voters in Their Place

Geography and Elections in Great Britain

By: Ron Johnston,Charles Pattie

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Putting Voters in Their Place

Geography and Elections in Great Britain

By: Ron Johnston,Charles Pattie

Using information from the UK elections, this title shows how voters and parties are affected by, and seek to influence, both national and local forces, placing the analysis of electoral behaviour into its geographical context.

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Page Count

357

Publisher

Oxford University Press, USA

Published Date

ISBN 10

0199268045

ISBN 13

9780199268047

The Real Positive Definite Completion Problem: Cycle Completability

Cycle Completability

By: Wayne Walton Barrett,Charles R. Johnson,Raphael Loewy

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The Real Positive Definite Completion Problem: Cycle Completability

Cycle Completability

By: Wayne Walton Barrett,Charles R. Johnson,Raphael Loewy

Given a partial symmetric matrix, the positive definite completion problem asks if the unspecified entries in the matrix can be chosen so as to make the resulting matrix positive definite. Applications include probability and statistics, image enhancement, systems engineering, geophysics, and mathematical programming. The positive definite completion problem can also be viewed as a mechanism for addressing a fundamental problem in Euclidean geometry: which potential geometric configurations of vectors (i.e., configurations with angles between some vectors specified) are realizable in a Euclidean space. The positions of the specified entries in a partial matrix are naturally described by a graph. The question of existence of a positive definite completion was previously solved completely for the restrictive class of chordal graphs and this work solves the problem for the class of cycle completable graphs, a significant generalization of chordal graphs. These are graphs for which knowledge of completability for induced cycles (and cliques) implies completability of partial symmetric matrices with the given graph.

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Publisher

American Mathematical Soc.

Published Date

ISBN 10

0821804731

ISBN 13

9780821804735

Visualization Handbook

By: Charles D. Hansen,Chris R. Johnson

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Visualization Handbook

By: Charles D. Hansen,Chris R. Johnson

The Visualization Handbook provides an overview of the field of visualization by presenting the basic concepts, providing a snapshot of current visualization software systems, and examining research topics that are advancing the field. This text is intended for a broad audience, including not only the visualization expert seeking advanced methods to solve a particular problem, but also the novice looking for general background information on visualization topics. The largest collection of state-of-the-art visualization research yet gathered in a single volume, this book includes articles by a "who's who of international scientific visualization researchers covering every aspect of the discipline, including:·Virtual environments for visualization·Basic visualization algorithms·Large-scale data visualization·Scalar data isosurface methods·Visualization software and frameworks·Scalar data volume rendering·Perceptual issues in visualization·Various application topics, including information visualization.* Edited by two of the best known people in the world on the subject; chapter authors are authoritative experts in their own fields;* Covers a wide range of topics, in 47 chapters, representing the state-of-the-art of scientific visualization.

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Page Count

1061

Publisher

Elsevier

Published Date

ISBN 10

0080481647

ISBN 13

9780080481647

Social Inequality

Forms, Causes, and Consequences

By: Heather M. Fitz Gibbon,Anne M. Nurse,Charles E. Hurst

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Social Inequality

Forms, Causes, and Consequences

By: Heather M. Fitz Gibbon,Anne M. Nurse,Charles E. Hurst

The eleventh edition of Social Inequality: Forms, Causes, and Consequences is an introduction to the study of social inequality. Fully updated statistics and examples convey the pervasiveness and extent of social inequality in the United States. The authors use an intersectional perspective to show how inequality occurs, how it affects all of us, and what is being done about it. With more resources and supplementary examples, exercises, and applications embedded throughout to aid students’ learning and visualization of important concepts, the book provides a rich theoretical treatment to address the current state of inequality. In line with current affairs, the authors have expanded the content to include: An intersectional approach throughout the chapters A stronger emphasis on the connections between poverty, wealth, and income inequality New case studies on the opioid epidemic, COVID-19, the lead poisoning crisis, and climate change A new focus on the rise of right-wing movements. With additional content and classroom extensions available online for instructors, Social Inequality remains an ideal and invaluable overview of the subject and provides undergraduate students with a robust understanding of social inequality from a sociological perspective.

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Page Count

574

Publisher

Taylor & Francis

Published Date

ISBN 10

1000626865

ISBN 13

9781000626865

Book's by Charles R. Johnson

Matrix Theory and Applications

Matrix Theory and Applications

Topics in Matrix Analysis

Topics in Matrix Analysis

Matrix Positivity

Matrix Positivity

Matrix Analysis

Matrix Analysis

Eigenvalues, Multiplicities and Graphs

Eigenvalues, Multiplicities and Graphs

Totally Nonnegative Matrices

Totally Nonnegative Matrices

Putting Voters in Their Place

Putting Voters in Their Place

The Real Positive Definite Completion Problem: Cycle Completability

The Real Positive Definite Completion Problem: Cycle Completability

Visualization Handbook

Visualization Handbook

Social Inequality

Social Inequality

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