Note on nonnegative 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.

On Reduced Rank Nonnegative Matrix Factorization for Symmetric Nonnegative Matrices

Let V ∈ R be a nonnegative matrix. The nonnegative matrix factorization (NNMF) problem consists of finding nonnegative matrix factors W ∈ R and H ∈ R such that V ≈ WH. Lee and Seung proposed two algorithms which find nonnegative W and H such that ‖V −WH‖F is minimized. After examining the case in which r = 1 about which a complete characterization of the solution is possible, we consider the ca...