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Books > Science & Mathematics > Mathematics > Geometry > Algebraic geometry
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Euclidean Distance Matrices and Their Applications in Rigidity Theory (Paperback, Softcover reprint of the original 1st ed. 2018)
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Euclidean Distance Matrices and Their Applications in Rigidity Theory (Paperback, Softcover reprint of the original 1st ed. 2018)
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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.
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