We describe a widely applicable method of grouping or clustering image features (such as points, lines, corners, flow vectors and the like). It takes as input a "proximity matrix" H a square, symmetric matrix of dimension N (where N is the number of features). The element i,j of H is an initial estimate of the "proximity" between the ith and yth features. As output it delivers another square sy...

a Nearly Tridiagonal Matrix Magdy Tawfik Hanna1 ABSTRACT A fully-fledged definition for the fractional discrete Fourier transform of type IV (FDFT-IV) is presented and shown to outperform the simple definition of the FDFT-IV which is proved to be just a linear combination of the signal, its DFT-IV and their flipped versions. This definition heavily depends on the availability of orthonormal eig...

The matrix representation of the set ∆(d), d = (d1, d2, d3), of the integers which are unrepresentable by d1, d2, d3 is found. The diagrammatic procedure of calculation of the generating function Φ ( d; z ) for the set ∆(d) is developed. The Frobenius number F ( d ) , genus G ( d ) and Hilbert series H(d; z) of a graded subring for non–symmetric and symmetric semigroups S ( d ) are found. The u...

Consider a convex set S = {x ∈ D : G(x) o 0} where G(x) is a symmetric matrix whose every entry is a polynomial or rational function, D ⊆ R is a domain on which G(x) is defined, and G(x) o 0 means G(x) is positive semidefinite. The set S is called semidefinite representable if it equals the projection of a higher dimensional set which is defined by a linear matrix inequality (LMI). This paper s...

The possible numbers of nonzero entries in a matrix with a given term rank are determined respectively in the generic case, the symmetric case and the symmetric case with 0’s on the main diagonal. The matrices that attain the largest number of nonzero entries are also determined.

In this paper, computational efficient technique is proposed to calculate the eigenvalues of a tridiagonal system matrix using Strum sequence and Gerschgorin theorem. The proposed technique is applicable in various control system and computer engineering applications. KeywordsEigenvalues, tridiagonal matrix, Strum sequence and Gerschgorin theorem. I.INTRODUCTION Solving tridiagonal linear syste...

In this paper for a given prescribed Ritz values that satisfy in the some special conditions, we find a symmetric nonnegative matrix, such that the given set be its Ritz values.

A set of fixed points of the Hopfield type neural network is under investigation. Its connection matrix is constructed with regard to the Hebb rule from a highly symmetric set of the memorized patterns. Depending on the external parameter the analytic description of the fixed points set has been obtained. A set of fixed points of the Hopfield type neural network is under investigation. Its conn...

Two matrix vector spaces V,W⊂Cn×n are said to be equivalent if SVR=W for some nonsingular S and R. These congruent R=ST. We prove that all matrices in V W symmetric, or skew-symmetric, then only they equivalent. Let F:U×…×U→V G:U′×…×U′→V′ symmetric skew-symmetric k-linear maps over C. If there exists a set of linear bijections φ1,…,φk:U→U′ ψ:V→V′ transforms F G, such with φ1=…=φk.