منابع مشابه
On distance matrices and Laplacians
We consider distance matrices of certain graphs and of points chosen in a rectangular grid. Formulae for the inverse and the determinant of the distance matrix of a weighted tree are obtained. Results concerning the inertia and the determinant of the distance matrix of an unweighted unicyclic graph are proved. If D is the distance matrix of a tree, then we obtain certain results for a perturbat...
متن کاملOn Euclidean distance matrices
If A is a real symmetric matrix and P is an orthogonal projection onto a hyperplane, then we derive a formula for the Moore-Penrose inverse of PAP . As an application, we obtain a formula for the MoorePenrose inverse of a Euclidean distance matrix (EDM) which generalizes formulae for the inverse of a EDM in the literature. To an invertible spherical EDM, we associate a Laplacian matrix (which w...
متن کاملSymmetric Laplacians, Quantum Density Matrices and their Von-Neumann Entropy
We show that the (normalized) symmetric Laplacian of a simple graph can be obtained from the partial trace over a pure bipartite quantum state that resides in a bipartite Hilbert space (one part corresponding to the vertices, the other corresponding to the edges). This suggests an interpretation of the symmetric Laplacian’s Von Neumann entropy as a measure of bipartite entanglement present betw...
متن کاملGraph-Laplacians and Dirac Operators and the Connes-Distance-Functional
We develop (within a possibly new) framework spectral analysis and operator theory on (almost) general graphs and use it to study spectral properies of the graph-Laplacian and so-called graph-Dirac-operators. That is, we introduce a Hilbert space structure, being in our framework the direct sum of a node-Hilbert-space and a bond-Hilbert-space, a Dirac operator intertwining these components, and...
متن کاملEla on Euclidean Distance Matrices of Graphs
Received by the editors on November 13, 2011. Accepted for publication on July 8, 2013. Handling Editor: Bryan L. Shader. FMF and IMFM, University of Ljubljana, Jadranska 19, 1000 Ljubljana, Slovenia, and IAM, University of Primorska, Slovenia ([email protected]). XLAB d.o.o., Pot za Brdom 100, 1125 Ljubljana, Slovenia, and FMF, University of Ljubljana, Slovenia ([email protected]...
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ژورنال
عنوان ژورنال: Linear Algebra and its Applications
سال: 2005
ISSN: 0024-3795
DOI: 10.1016/j.laa.2004.05.011