Authors:
- Offers a comprehensive and accessible exposition of Euclidean Distance Matrices (EDMs) and rigidity theory of bar-and-joint frameworks
- Highlights two parallel approaches to rigidity theory that lend themselves easily to semidefinite programming machinery
- Includes numerous examples that illustrate important theorems and concepts
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Table of contents (10 chapters)
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Front Matter
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Back Matter
About this book
Euclidean Distance Matrices and Their Applications in Rigidity Theory begins by establishing the necessary background needed for the rest of the book. The focus of Chapter 1 is on pertinent results from matrix theory, graph theory and convexity theory, while Chapter 2 is devoted to positive semidefinite (PSD) matrices due to the key role these matrices play in ourapproach. Chapters 3 to 7 provide detailed studies of EDMs, and in particular their various characterizations, classes, eigenvalues and geometry. Chapter 8 serves as a transitional chapter between EDMs and rigidity theory. Chapters 9 and 10 cover local and universal rigidities of bar-and-joint frameworks. This book is self-contained and should be accessible to a wide audience including students and researchers in statistics, operations research, computational biochemistry, engineering, computer science and mathematics.
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Authors and Affiliations
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Department of Mathematics and Statistics, University of Windsor, Windsor, Canada
Abdo Y. Alfakih
About the author
Bibliographic Information
Book Title: Euclidean Distance Matrices and Their Applications in Rigidity Theory
Authors: Abdo Y. Alfakih
DOI: https://doi.org/10.1007/978-3-319-97846-8
Publisher: Springer Cham
eBook Packages: Mathematics and Statistics, Mathematics and Statistics (R0)
Copyright Information: Springer Nature Switzerland AG 2018
Hardcover ISBN: 978-3-319-97845-1Published: 22 October 2018
Softcover ISBN: 978-3-030-07417-3Published: 19 January 2019
eBook ISBN: 978-3-319-97846-8Published: 13 October 2018
Edition Number: 1
Number of Pages: XIV, 251
Number of Illustrations: 28 b/w illustrations
Topics: Statistical Theory and Methods, Convex and Discrete Geometry, Discrete Mathematics in Computer Science