This paper is concerned with the distance of a symmetric tridiagonal Toeplitz matrix $T$ to manifold similarly structured singular matrices, and determining closest in this manifold. Explicit formulas are presented, exploiting analysis sensitivity spectrum respect structure-preserving perturbations its entries.

It is known from algebraic graph theory that if L the Laplacian matrix of some tree G with a vertex degree sequence d=(δ1,…,δn)⊤ and D its distance matrix, then LD+2I=(2⋅1−d)1⊤, where 1 an all-ones column vector. We prove converse proposition: this identity holds for d D, essentially tree, matrix. This result immediately generalizes to weighted graphs. Therefore, above bilinear equation in L, c...

Many combinatorial configurations (for example, perfect codes, latin squares and hypercubes, combinatorial designs and their q-ary generalizations — subspace designs) can be defined as an eigenfunction on a graph with some discrete restrictions. The study of these configurations often leads to the question about the minimum possible difference between two configurations from the same class (it ...

For objects in general metric spaces, the generalized hyperplane indexing is one of the most widely used indexing techniques In the paper, some methods are presented to improve the quality of the partitioning in generalized hyperplane tree structure from the viewpoint of balancing factor. The proposed method to represent the elements in the target domain metric space is the usage of a distance ...

Coding schemes are presented that provide the ability to correct and detect computational errors while using dotproduct engines for integer vector–matrix multiplication. Both the L1-metric and the Hamming metric are considered.

It is shown that distance powers of an integral Cayley graph over an abelian group Γ are again integral Cayley graphs over Γ. Moreover, it is proved that distance matrices of integral Cayley graphs over abelian groups have integral spectrum.

A computationally efficient method for detecting a chorus section in popular and rock music is presented. The method utilizes a distance matrix representation that is obtained by summing two separate distance matrices calculated using the mel-frequency cepstral coefficient and pitch chroma features. The benefit of computing two separate distance matrices is that different enhancement operations...