A formula for the distance of a Toeplitz matrix to the subspace of {e}-circulant matrices is presented, and applications of {e}-circulant matrices to preconditioning of linear systems of equations with a Toeplitz matrix are discussed. Copyright c © 2006 John Wiley & Sons, Ltd. key words: Toeplitz matrix, circulant matrix, {e}-circulant, matrix nearness problem, distance to normality, preconditi...

In their 1978 paper \Distance Matrix Polynomials of Trees", [4], Graham and Lov asz proved that the coeÆcients of the characteristic polynomial of the distance matrix of a tree (CPD(T )) can be expressed in terms of the numbers of certain subforests of the tree. This result was generalized to trees with weighted edges by Collins, [1], in 1986. Graham and Lov asz computed these coeÆcients for al...

Short proofs are given to various characterizations of the (circum-)Euclidean squared distance matrices. Linear preserver problems related to these matrices are discussed.

Spatial mobility is a topical concept of analytical migration science, which makes it possible to assess the desires, readiness and capabilities of the population to move over certain distances and time. In the management of spatial mobility assessment requires the organization of systematic monitoring, which includes identifying the mobility potential in spatial and temporal interpretation, th...

We introduce the concept of distance mean-regular graph, which can be seen as a generalization of both vertex-transitive and distance-regular graphs. A graph Γ = (V,E) with diameter D is distance meanregular when, for given u ∈ V , the averages of the intersection numbers ai(u, v), bi(u, v), and ci(u, v) (defined as usual), computed over all vertices v at distance i = 0, 1, . . . , D from u, do...

Non-deterministic matrices, a natural generalization of many-valued matrices, are semantic structures in which the value assigned to a complex formula may be chosen non-deterministically from a given set of options. We show that by combining non-deterministic matrices and distance-based considerations, one obtains a family of logics that are useful for reasoning with uncertainty. These logics a...

Short proofs are given to various characterizations of the (circum-)Euclidean squared distance matrices. Linear preserver problems related to these matrices are discussed.

During the search for new structural descriptors we have defined the information-theory operators U(M), V(M), X(M), and Y(M), that are computed from atomic invariants and measure the information content of the elements of molecular matrices. Structural descriptors computed with these four information-theory operators are used to develop structure-property models for the boiling temperature, mol...

The component matrix, Laplacian Distance Peripheral distance of the cyclotomic graphs and some properties are found. D-energy, $D_{p}$-energy, $D^{L}$-energy indices determined. For real symmetric matrices, matrices that attain maximum $L, L_{s}$ minimum S calculated. Hausdorff optimal matching evaluated.