Generalized diagonal dominance, a specific property of the matrix, can be very useful in various fields of the applied linear algebra, as a tool for discovering and proving new results. First, it gives possibility to be able to define different subclasses of H-matrices (papers [3], [11]). Second, it suggests a way to deduce and prove new theorems on the eigenvalue localization (papers [2], [4],...

We characterize the accuracy of a cooperative localization algorithm based on Kalman Filtering, as expressed by the trace of the covariance matrix, in terms of the algebraic graph theoretic properties of the sensing graph. In particular, we discover a weighted Laplacian in the expression that yields the constant, steady state value of the covariance matrix. We show how one can reduce the locali...

It is well known that the spectrum of a given matrix A belongs to the Geršgorin set (A), as well as to the Geršgorin set applied to the transpose of A, (AT). So, the spectrum belongs to their intersection. But, if we first intersect i-th Geršgorin disk i(A) with the corresponding disk i(A), and then we make union of such intersections, which are, in fact, the smaller disks of each pair, what we...

In this paper, we investigatethe boundary value problem for differential pencils on the half-linewith a turning point. Using a fundamental system of solutions, wegive a asymptotic distribution of eigenvalues.

In this paper some upper and lower bounds for the greatest eigenvalues of the PI and vertex PI matrices of a graph G are obtained. Those graphs for which these bounds are best possible are characterized.

We define a random-matrix ensemble given by the infinite-time covariance matrices of Ornstein-Uhlenbeck processes at different temperatures coupled by a Gaussian symmetric matrix. The spectral properties of this ensemble are shown to be in qualitative agreement with some stylized facts of financial markets. Through the presented model formulas are given for the analysis of heterogeneous time se...

The D-eigenvalues {µ1,…,µp} of a graph G are the eigenvalues of its distance matrix D and form its D-spectrum. The D-energy, ED(G) of G is given by ED (G) =∑i=1p |µi|. Two non cospectral graphs with respect to D are said to be D-equi energetic if they have the same D-energy. In this paper we show that if G is an r-regular graph on p vertices with 2r ≤ p - 1, then the complements of iterated lin...

The direct position determination approach was recently presented as a promising technique for the localization of a transmitting source with accuracy higher than that of the conventional two-step localization method. In this paper, the theoretical performance of a direct position determination estimator proposed by Weiss is examined for situations in which the array model errors are present. O...

We study the energy minima of fully-connected $m$-components vector spin glass model at zero temperature in an external magnetic field for $m\ge 3$. The has a transition from paramagnetic phase high to low field. eigenvalues and eigenvectors Hessian Hamiltonian. spectrum is gapless both phase, with pseudo-gap behaving as $\lambda^{m-1}$ $\sqrt{\lambda}$ phase. Despite long-range nature model, e...