On Euclidean distance matrices

DOI10.1016/j.laa.2006.05.013zbMath1118.15024OpenAlexW2077002005MaRDI QIDQ884414

Ramamurthy Balaji, Ravindra B. Bapat

Publication date: 6 June 2007

Published in: Linear Algebra and its Applications (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.laa.2006.05.013

zbMATH Keywords

LaplaciantreesMoore-Penrose inverseLaplacian matrixEuclidean distance matrixinfinitely divisible matrices

Mathematics Subject Classification ID

Trees (05C05) Theory of matrix inversion and generalized inverses (15A09) Graphs and linear algebra (matrices, eigenvalues, etc.) (05C50) Hermitian, skew-Hermitian, and related matrices (15B57)

Related Items (15)

On distance matrices of wheel graphs with an odd number of vertices ⋮ Determining finite connected graphs along the quadratic embedding constants of paths ⋮ On quadratic embedding constants of star product graphs ⋮ Quadratic embedding constants of graph joins ⋮ Hyperspherical embedding of graphs and networks in communicability spaces ⋮ Complete multipartite graphs of non-QE class ⋮ Bilinear matrix equation characterizes Laplacian and distance matrices of weighted trees ⋮ Moore-Penrose inverse of a Euclidean distance matrix ⋮ A feasible \(k\)-means kernel trick under non-Euclidean feature space ⋮ Moore-Penrose inverse of a hollow symmetric matrix and a predistance matrix ⋮ Characterization of symmetric \(M\)-matrices as resistive inverses ⋮ On the Existence of Kernel Function for Kernel-Trick of k-Means ⋮ On unit spherical Euclidean distance matrices which differ in one entry ⋮ Every nonsingular spherical Euclidean distance matrix is a resistance distance matrix ⋮ Distance matrices and quadratic embedding of graphs

Cites Work

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• Properties of Euclidean and non-Euclidean distance matrices
• Methods for constructing distance matrices and the inverse eigenvalue problem
• Distance matrix polynomials of trees
• On distance matrices and Laplacians
• Connections between the real positive semidefinite and distance matrix completion problems
• Criteria for quasi-convexity and pseudo-convexity: Relationships and comparisons
• Infinitely Divisible Matrices
• The Theory of Infinitely Divisible Matrices and Kernels
• On the Addressing Problem for Loop Switching
• Metric Spaces and Positive Definite Functions
• N-matrices
• Inequalities and equalities associated with the Campbell-Youla generalized inverse of the indefinite admittance matrix of resistive networks

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