In this paper, block distance matrices are introduced. Suppose F is a square block matrix in which each block is a symmetric matrix of some given order. If F is positive semidefinite, the block distance matrix D is defined as a matrix whose (i, j)-block is given by D ij = F ii +F jj −2F ij. When each block in F is 1 × 1 (i.e., a real number), D is a usual Euclidean distance matrix. Many interes...

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...

The Mantel test is widely used to test the linear or monotonic independence of the elements in two distance matrices. It is one of the few appropriate tests when the hypothesis under study can only be formulated in terms of distances; this is often the case with genetic data. In particular, the Mantel test has been widely used to test for spatial relationship between genetic data and spatial la...

In the practice of information extraction, the input data are usually arranged into pattern matrices, and analyzed by the methods of linear algebra and statistics, such as principal component analysis. In some applications, the tacit assumptions of these methods lead to wrong results. The usual reason is that the matrix composition of linear algebra presents information as flowing in waves, whe...

introduction: under the principles of international law, no state has the right to use or permit the use of its territory in such a manner as to cause damage to the environment of other states. spatial econometrics provides a powerful tool to assess the influence of the pollution of neighboring countries on a country's pollution level. spatial spillover effects play a significant role in a...

residential location choice modeling is one of the areas in transportation planning that attempts to examine households location search behavior incorporating their trade-offs between housing quality, prices or rents, distance to work and other key factors. this brings up the need to come up with methods to logically allocate credible choice alternatives for individuals.this article attempts to...

abstract soil invertebrate and their spatial pattern are affected strongly by environmental factors. spatial variability of soil properties is one of the most important reasons of the macrofauna variability. this study was conducted to investigate the spatial variability of soil properties and soil macrofauna biomass in the riparian forest landscape of karkhe river. soil macro fauna were sample...

Spatial and temporal contextual information plays a key role for analyzing user behaviors, and is helpful for predicting where he or she will go next. With the growing ability of collecting information, more and more temporal and spatial contextual information is collected in systems, and the location prediction problem becomes crucial and feasible. Some works have been proposed to address this...