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Titlebook: Euclidean Distance Matrices and Their Applications in Rigidity Theory; Abdo Y. Alfakih Book 2018 Springer Nature Switzerland AG 2018 Eucli

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書目名稱Euclidean Distance Matrices and Their Applications in Rigidity Theory
編輯Abdo Y. Alfakih
視頻videohttp://file.papertrans.cn/317/316422/316422.mp4
概述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 t
圖書封面Titlebook: Euclidean Distance Matrices and Their Applications in Rigidity Theory; Abdo Y. Alfakih Book 2018 Springer Nature Switzerland AG 2018 Eucli
描述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 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. Chapter
出版日期Book 2018
關(guān)鍵詞Euclidean Distance Matrix; Euclidean Distance Matrices; EDMs; Spherical EDMs; Eigenvalues of EDMs; Multid
版次1
doihttps://doi.org/10.1007/978-3-319-97846-8
isbn_softcover978-3-030-07417-3
isbn_ebook978-3-319-97846-8
copyrightSpringer Nature Switzerland AG 2018
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Preliminaries: Basics and Notation,mming distance matrices on the hypercube, distance matrices of trees and resistance distance matrices of electrical networks. The second part focuses on nonspherical EDMs and their characterization. As an interesting example of nonspherical EDMs, we discuss multispherical EDMs.
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Classes of EDMs,mming distance matrices on the hypercube, distance matrices of trees and resistance distance matrices of electrical networks. The second part focuses on nonspherical EDMs and their characterization. As an interesting example of nonspherical EDMs, we discuss multispherical EDMs.
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https://doi.org/10.1007/978-3-319-30681-0lated to eigenvalues such as: a method for constructing nonisomorphic cospectral EDMs; the connection between EDMs, graphs, and combinatorial designs; EDMs with exactly two or three distinct eigenvalues and the EDM inverse eigenvalue problem.
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發(fā)表于 2025-3-23 07:43:52 | 只看該作者
S. Saltiel,K. Koynov,I. Buchvarov explicit formulas for the intervals, within which, entries can vary, one at a time, if the matrix is to remain an EDM. Moreover, we present a characterization of those entries whose intervals have zero length; i.e., those entries where any deviation from their current values renders the matrix non-EDM.
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