Group characters and nonnegative integral matrices

Double Coset Matrices and Group Characters

Characteristic Polynomials of Nonnegative Integral Square Matrices and Clique Polynomials

Clique polynomials of vertex-weighted simple graphs coincide with polynomials of the form det(1 − xM), M a square matrix over N.

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.

Monotonicity of Nonnegative Matrices

We present a nonnegative rank factorization of a nonnegative matrix A for the case in which one or both of A(1)A and AA(1) are nonnegative. This gives, in particular, a known result for characterizing nonnegative matrices when A†A or AA† is nonnegative. We applied this characterization to the derivation of known results based on the characterization of nonnegative monotone matrices. A matrix A ...

Which Nonnegative Matrices Are Slack Matrices?

In this paper we characterize the slack matrices of cones and polytopes among all nonnegative matrices. This leads to an algorithm for deciding whether a given matrix is a slack matrix. The underlying decision problem is equivalent to the polyhedral verification problem whose complexity is unknown.