3 citations · 9 across the 11 of their papers we have counts for
13 papers
Optimization problem for star covers of graphs without four cycles
Damjana Kokol Bukovšek, Polona Oblak, Helena Šmigoc
This work presents a study of star covers on graphs. Unlike traditional formulations that minimize the number of stars, our aim is to optimize the number of bipartite components us…
Arbitrarily Finely Divisible Matrices
Priyanka Joshi, Helena Šmigoc
The class of stochastic matrices that have a stochastic -th root for infinitely many natural numbers is introduced and studied. Such matrices are called arbitrarily finely d…
Paths are generically realisable
Rupert H. Levene, Polona Oblak, Helena Šmigoc
We show that every - multiplicity matrix for a simple graph is generically realisable for . In particular, every multiplicity matrix for a path is generically realisab…
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…
Integer completely positive matrices of order two
Thomas Laffey, Helena Šmigoc
We show that every integer doubly nonnegative matrix has an integer cp-factorization.
Nonnegative Factorization of a Data Matrix as a Motivational Example for Basic Linear Algebra
Barak A. Pearlmutter, Helena Šmigoc
We present a motivating example for matrix multiplication based on factoring a data matrix. Traditionally, matrix multiplication is motivated by applications in physics: composing…
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…
An extension of the Hermite-Biehler theorem with application to polynomials with one positive root
Richard Ellard, Helena Šmigoc
If a real polynomial is Hurwitz stable (every root if lies in the open left half-plane), then the Hermite-Biehler Theorem says that the polynomials $p(-x^…
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…