A note on nonnegative normal matrices

A note on nonnegative diagonally dominant matrices

On the nonnegative inverse eigenvalue problem of traditional matrices

In this paper, at first for a given set of real or complex numbers $sigma$ with nonnegative summation, we introduce some special conditions that with them there is no nonnegative tridiagonal matrix in which $sigma$ is its spectrum. In continue we present some conditions for existence such nonnegative tridiagonal matrices.

On Nonnegative Factorization of Matrices

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

Nonnegative Matrices

For a loopless, acyclic, transitive directed graph S, we study the relations between the predecessor property and the well structured property on S. These properties assure the existence of nonnegativ€ Jordan bases for any nonnegative matrix with singular graph S.

A note on the convexity of the realizable set of eigenvalues for nonnegative symmetric matrices

Geometric properties of the set Rn of n–tuples of realizable spectra of nonnegative symmetric matrices, and the Soules set Sn introduced by McDonald and Neumann, are examined. It is established that S5 is properly contained in R5. Two interesting examples are presented which show that neither Rn nor Sn need be convex. It is proved that Rn and Sn are star convex and centered at (1, 1, . . . , 1).