The least upper bound for the norm distance between two normal matrices is given in terms of their eigenvalues exclusively, thus solving a problem which appears to be long open.

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...

Multidimensional Scaling (MDS) is a classic technique that seeks vectorial representations for data points, given the pairwise distances between them. However, in recent years, data are usually collected from diverse sources or have multiple heterogeneous representations. How to do multidimensional scaling on multiple input distance matrices is still unsolved to our best knowledge. In this pape...

For 1990–2019, this study presents two-step GMM estimates of EU members’ demands for defense spending based on alternative spatial-weight matrices. In particular, spatial connectivity is tied to membership status, contiguity, contiguity and power projection, inverse distance, arms trade. At a Nash equilibrium, our demand equations are derived explicitly from spatially game-theoretical model all...