TY - BOOK ID - 33226812 TI - Euclidean Distance Matrices and Their Applications in Rigidity Theory PY - 2018 SN - 3319978462 3319978454 PB - Cham : Springer International Publishing : Imprint: Springer, DB - UniCat KW - Rigidity (Geometry) KW - Matrices. KW - Geometric rigidity KW - Rigidity theorem KW - Discrete geometry KW - Algebra, Matrix KW - Cracovians (Mathematics) KW - Matrix algebra KW - Matrixes (Algebra) KW - Algebra, Abstract KW - Algebra, Universal KW - Mathematical statistics. KW - Discrete groups. KW - Computational complexity. KW - Statistical Theory and Methods. KW - Convex and Discrete Geometry. KW - Discrete Mathematics in Computer Science. KW - Complexity, Computational KW - Electronic data processing KW - Machine theory KW - Groups, Discrete KW - Infinite groups KW - Mathematics KW - Statistical inference KW - Statistics, Mathematical KW - Statistics KW - Probabilities KW - Sampling (Statistics) KW - Statistical methods KW - Discrete mathematics KW - Statistics . KW - Convex geometry . KW - Discrete geometry. KW - Computer science—Mathematics. KW - Geometry KW - Combinatorial geometry KW - Statistical analysis KW - Statistical data KW - Statistical science KW - Econometrics UR - https://www.unicat.be/uniCat?func=search&query=sysid:33226812 AB - 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 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. ER -