On yielding and jointly yielding entries of Euclidean distance matrices

On Yielding and Jointly Yielding Entries of Euclidean Distance Matrices

Abstract An n × n matrix D is a Euclidean distance matrix (EDM) if there exist p, . . . , pn in some Euclidean space such that dij = ||pi − pj ||2 for all i, j = 1, . . . , n. Let D be an EDM and let Eij be the n×n symmetric matrix with 1’s in the ijth and jith entries and 0’s elsewhere. We say that [lij , uij ] is the yielding interval of entry dij if it holds that D+ tE ij is an EDM if and on...

On 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...

Ela 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]...

On Euclidean distance matrices of graphs

On the eigenvalues of Euclidean distance matrices

In this paper, the notion of equitable partitions (EP) is used to study the eigenvalues of Euclidean distance matrices (EDMs). In particular, EP is used to obtain the characteristic polynomials of regular EDMs and non-spherical centrally symmetric EDMs. The paper also presents methods for constructing cospectral EDMs and EDMs with exactly three distinct eigenvalues. Mathematical subject classif...