It is shown that a sufficient condition for a nonnegative real symmetric matrix to be completely positive is that the matrix is diagonally dominant.

The paper studies the eigenvalue distribution of some special matrices, including block diagonally dominant matrices and block H−matrices. A well-known theorem of Taussky on the eigenvalue distribution is extended to such matrices. Conditions on a block matrix are also given so that it has certain numbers of eigenvalues with positive and negative real parts.

Higher-dimensional symmetric games become of more and more importance for applied microand macroeconomic research. Standard approaches to uniqueness of equilibria have the drawback that they are restrictive or not easy to evaluate analytically. In this paper I provide some general but comparably simple tools to verify whether a symmetric game has a unique symmetric equilibrium or not. I disting...

We establish upper and lower bounds for the entries of the inverses of diagonally dominant tridiagonal matrices. These bounds improve the bounds recently given by Shivakumar and Ji. Moreover, we show how to improve our bounds iteratively. For an n n M{matrix this iterative reenement yields the exact inverse after n ? 1 steps.

Systems of linear diierential equations with constant coeecients, as well as Lotka{Volterra equations, with delays in the oo{diagonal terms are considered. Such systems are shown to be asymptotically stable for any choice of delays if and only if the matrix has a negative weakly dominant diagonal.

In this paper, we present some new upper bounds for the spectral radius of iterative matrices based on the concept of doubly α diagonally dominant matrix. And subsequently, we give two examples to show that our results are better than the earlier ones. Keywords—doubly α diagonally dominant matrix, eigenvalue, iterative matrix, spectral radius, upper bound.

For a symmetric positive semi-definite diagonally dominant matrix, if its off-diagonal entries and its diagonally dominant parts for all rows (which are defined for a row as the diagonal entry subtracted by the sum of absolute values of off-diagonal entries in that row) are known to a certain relative accuracy, we show that its eigenvalues are known to the same relative accuracy. Specifically, ...

It is well known, see [D. Carlson, T. Markham, Schur complements of diagonally dominant matrices, Czech. Math. Schur complement of a strictly diagonally dominant matrix is strictly diagonally dominant , as well as its diagonal-Schur complement. Also, if a matrix is an H-matrix, then its Schur complement and diagonal-Schur complement are H-matrices, too, see [J. Liu, Y. Huang, Some properties on...

In Gao and Huang [Z.X. Gao, T.Z Huang, Convergence of AOR method, Appl. Math. Comput. 176 (2006) 134–140] some practical sufficient conditions for the convergence of the AOR (accelerated overrelaxation) method for solving linear system Ax 1⁄4 b, with A being doubly diagonally dominant matrix, are presented. Using a different approach we will give some improvements in both cases, when the matrix...