Euclidean Distance Matrices and Their Applications in Rigidity Theory

• Main Author: Alfakih, Abdo Y. (Author, http://id.loc.gov/vocabulary/relators/aut)
• Corporate Author: SpringerLink (Online service)
• Format: Electronic eBook
• Language: English
• Published: Cham : Springer International Publishing : Imprint: Springer, 2018.
• Edition: 1st ed. 2018.
• Subjects: Statistics .; Convex geometry .; Discrete geometry.; Computer science-Mathematics.; Statistical Theory and Methods.; Convex and Discrete Geometry.; Discrete Mathematics in Computer Science.

This book offers a comprehensive and accessible exposition of Euclidean Distance Matrices (EDMs) and rigidity theory of bar-and-joint frameworks. It is based on the one-to-one correspondence between EDMs and projected Gram matrices. Accordingly the machinery of semidefinite programming is a common t...

Table of Contents:

• Chapter 1. Mathematical Preliminaries
• Chapter 2. Positive Semidefinite Matrices
• Chapter 3. Euclidean Distance Matrices (EDMs)
• Chapter 4. Classes of EDMs
• Chapter 5. The Geometry of EDMs
• Chapter 6. The Eigenvalues of EDMs
• Chapter 7. The Entries of EDMs
• Chapter 8. EDM Completions and Bar Frameworks
• Chapter 9. Local and Infinitesimal Rigidities
• Chapter 10. Universal and Dimensional Rigidities
• Epilogue.