In this paper, we obtain a theorem on the distribution of eigenvalues for Schur complements of H-matrices. Further, we give some properties of diagonal-Schur complements on diagonally dominant matrices and their distribution of eigenvalues. © 2004 Elsevier Inc. All rights reserved. AMS classification: 15A45; 15A48

Conditions are given which guarantee that the k-subdirect sum of S-strictly diagonally dominant matrices (S-SDD) is also S-SDD. The same situation is analyzed for SDD matrices. The converse is also studied: given an SDD matrix C with the structure of a k-subdirect sum and positive diagonal entries, it is shown that there are two SDD matrices whose subdirect sum is C. AMS subject classifications...

We establish two sufficient conditions for the stability of a P -matrix. First, we show that a P -matrix is positive stable if its skew-symmetric component is sufficiently smaller (in matrix norm) than its symmetric component. This result generalizes the fact that symmetric P -matrices are positive stable, and is analogous to a result by Carlson which shows that sign symmetric P -matrices are p...

In this paper, we present a new property for the α diagonally dominant matrix. As applications, we give some criteria to distinguish the nosingular H-matrix. Mathematics Subject Classification: 15A47

Let M(A) denote the comparison matrix of a square H-matrix A, that is, M(A) is an M-matrix. Hmatrices such that their comparison matrices are non-singular are well studied in the literature. In this paper, we study characterizations of H-matrices with either singular or non-singular comparison matrices. The spectral radius of the Jacobi matrix of M(A) and the generalized diagonal dominance prop...

One of the classical maximum principles state that any nonnegative solution of a proper elliptic PDE attains its maximum on the boundary of a bounded domain. We suitably extend this principle to nonlinear cooperative elliptic systems with diagonally dominant coupling and with mixed boundary conditions. One of the consequences is a preservation of nonpositivity, i.e. if the coordinate functions ...

This paper proposes the definition of the generalized Schur complement on nonstrictly diagonally dominant matrices and general H−matrices by using a particular generalized inverse, and then, establishes some significant results on heredity, nonsingularity and the eigenvalue distribution for these generalized Schur complements.

Let I ⊆ R be an interval and let k : I2 → C be a reproducing kernel on I . We show that if k(x, y) is in the appropriate differentiability class, it satisfies a 2-parameter family of inequalities of which the diagonal dominance inequality for reproducing kernels is the 0th order case. We provide an application to integral operators: if k is a positive definite kernel on I (possibly unbounded) w...

This paper proposes the definition of the generalized Schur complement on nonstrictly diagonally dominant matrices and general H−matrices by using a particular generalized inverse, and then, establishes some significant results on heredity, nonsingularity and the eigenvalue distribution for these generalized Schur complements.

A hidden positive row diagonally dominant (hprdd) matrix is a square matrix A for which there exist square matrices C and B so that AC = B and each diagonal entry of B and C is greater than the sum of the absolute values of the off-diagonal entries in its row. A linear program with 5n2 − 4n variables and 2n2 constraints is defined that takes as input an n × n matrix A and produces C and B satis...