Overview
- 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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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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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