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010   $a3-319-97846-2
024 7 $a10.1007/978-3-319-97846-8
035   $a(CKB)4100000007003149
035   $a(MiAaPQ)EBC5554521
035   $a(DE-He213)978-3-319-97846-8
035   $a(PPN)231464460
035   $a(EXLCZ)994100000007003149
100   $a20181013d2018      u|         0
101 0 $aeng
135   $aurcnu||||||||
181   $ctxt$2rdacontent
182   $cc$2rdamedia
183   $acr$2rdacarrier
200 10$aEuclidean Distance Matrices and Their Applications in Rigidity Theory /$fby Abdo Y. Alfakih
205   $a1st ed. 2018.
210  1$aCham :$cSpringer International Publishing :$cImprint: Springer,$d2018.
215   $a1 online resource (xiv, 251 pages) $cillustrations
311 08$a3-319-97845-4 
327   $aChapter 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.
330   $aThis 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 thread that runs throughout the book. As a result, two parallel approaches to rigidity theory are presented. The first is traditional and more intuitive approach that is based on a vector representation of point configuration. The second is based on a Gram matrix representation of point configuration. 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 our approach. 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.
606   $aStatistics
606   $aConvex geometry
606   $aDiscrete geometry
606   $aComputer science$xMathematics
606   $aDiscrete mathematics
606   $aStatistical Theory and Methods
606   $aConvex and Discrete Geometry
606   $aDiscrete Mathematics in Computer Science
615  0$aStatistics.
615  0$aConvex geometry.
615  0$aDiscrete geometry.
615  0$aComputer science$xMathematics.
615  0$aDiscrete mathematics.
615 14$aStatistical Theory and Methods.
615 24$aConvex and Discrete Geometry.
615 24$aDiscrete Mathematics in Computer Science.
676   $a516.11
700   $aAlfakih$b Abdo Y$4aut$4http://id.loc.gov/vocabulary/relators/aut$0768240
906   $aBOOK
912   $a9910300131503321
996   $aEuclidean Distance Matrices and Their Applications in Rigidity Theory$92056066
997   $aUNINA