3 citations · 9 across the 11 of their papers we have counts for
7 papers · 1 filter
The integer cp-rank of matrices
Thomas Laffey, Helena Šmigoc
We show the cp-rank of an integer doubly nonnegative matrix does not exceed .
Diagonal realizability in the Nonnegative Inverse Eigenvalue Problem
Thomas J. Laffey, Helena Šmigoc
We show that if a list of nonzero complex numbers is the nonzero spectrum of a diagonalizable nonnegative matrix, then is the nonzero spectrum of a dia…
Diagonal elements in the Nonnegative Inverse Eigenvalue Problem
Richard Ellard, Helena Šmigoc
We say that a list of complex numbers is "realisable" if it is the spectrum of some (entrywise) nonnegative matrix. The Nonnegative Inverse Eigenvalue Problem (NIEP) is the problem…
The maximum of the minimal multiplicity of eigenvalues of symmetric matrices whose pattern is constrained by a graph
Polona Oblak, Helena Šmigoc
In this paper we introduce a parameter , defined as the maximum over the minimal multiplicities of eigenvalues among all symmetric matrices corresponding to a graph . We…
Connecting sufficient conditions for the Symmetric Nonnegative Inverse Eigenvalue Problem
Richard Ellard, Helena Šmigoc
We say that a list of real numbers is "symmetrically realisable" if it is the spectrum of some (entrywise) nonnegative symmetric matrix. The Symmetric Nonnegative Inverse Eigenvalu…
Graphs that allow all the eigenvalue multiplicities to be even
Polona Oblak, Helena Šmigoc
Let be an undirected graph on vertices and let be the set of all real symmetric matrices whose nonzero off-diagonal entries occur in exactly the positio…
Constructing New Realisable Lists from Old in the NIEP
Richard Ellard, Helena Šmigoc
Given a list of complex numbers σ:=(λ_1,λ_2,...,λ_m), we say that σ is realisable if σ is the spectrum of some (entrywise) nonnegative matrix. The Nonnegative Inverse Eigenvalue Pr…