Helena Šmigoc

activity

20122026

most citedSymmetric Nonnegative Matrix Trifactorization

6 citations · 14 across the 14 of their papers we have counts for

collaborators

18 papers

math.SP2026

A note on Guo's perturbation result for symmetric nonnegative matrices

Helena Šmigoc

In 1997 Guo Wuwen proved that if $(λ_{1}, λ_{2}, \dots, λ_{n})$ is the spectrum of a nonnegative matrix with Perron eigenvalue $λ_{1}$ and $λ_{2}$ real, then $(λ_{1} + t, λ_{2} \pm t, λ_{3}, \dots, λ_{n})$ is…

math.CO2025

Orthogonalisability of joins of graphs

Rupert H. Levene, Polona Oblak, Helena Šmigoc

A graph is said to be orthogonalisable if the set of real symmetric matrices whose off-diagonal pattern is prescribed by its edges contains an orthogonal matrix. We determine some…

math.CO2023★ 2 cited

Symmetric Nonnegative Trifactorization of Pattern Matrices

Damjana Kokol Bukovšek, Helena Šmigoc

A factorization of an $n \times n$ nonnegative symmetric matrix $A$ of the form $B C B^{T}$ , where $C$ is a $k \times k$ symmetric matrix, and both $B$ and $C$ are required to be nonne…

math.CO2023

Powers of Karpelevic arcs and their Sparsest Realising matrices

Priyanka Joshi, Stephen Kirkland, Helena Smigoc

The region in the complex plane containing the eigenvalues of all stochastic matrices of order n was described by Karpelevic in 1988, and it is since then known as the Karpelevic r…

math.CO2023★ 1 cited

Bordering of Symmetric Matrices and an Application to the Minimum Number of Distinct Eigenvalues for the Join of Graphs

Aida Abiad, Shaun M. Fallat, Mark Kempton +5

An important facet of the inverse eigenvalue problem for graphs is to determine the minimum number of distinct eigenvalues of a particular graph. We resolve this question for the j…

math.CO2023

The liberation set in the inverse eigenvalue problem of a graph

Jephian C. -H. Lin, Polona Oblak, Helena Šmigoc

The inverse eigenvalue problem of a graph $G$ is the problem of characterizing all lists of eigenvalues of real symmetric matrices whose off-diagonal pattern is prescribed by the a…

math.CO2023

Spectral arbitrariness for trees fails spectacularly

Shaun M. Fallat, H. Tracy Hall, Rupert H. Levene +4

If $G$ is a graph and $m$ is an ordered multiplicity list which is realizable by at least one symmetric matrix with graph $G$ , what can we say about the eigenvalues of all…

math.SP2021

Stochastic Matrices Realising the Boundary of the Karpelevi\v c Region

Stephen Kirkland, Helena Šmigoc

A celebrated result of Karpelevi\v c describes $Θ_{n},$ the collection of all eigenvalues arising from the stochastic matrices of order $n .$ The boundary of $Θ_{n}$ consists of roots o…

math.OC2021★ 6 cited

Symmetric Nonnegative Matrix Trifactorization

Damjana Kokol Bukovšek, Helena Šmigoc

The Symmetric Nonnegative Matrix Trifactorization (SN-Trifactorization) is a factorization of an $n \times n$ nonnegative symmetric matrix $A$ of the form $B C B^{T}$ , where $C$ is a $…

math.CO2020★ 1 cited

Orthogonal symmetric matrices and joins of graphs

Rupert H. Levene, Polona Oblak, Helena Šmigoc

We introduce a notion of compatibility for multiplicity matrices. This gives rise to a necessary condition for the join of two (possibly disconnected) graphs $G$ and $H$ to be the…

math.CO2020

On the inverse eigenvalue problem for block graphs

Jephian C. -H. Lin, Polona Oblak, Helena Šmigoc

The inverse eigenvalue problem of a graph $G$ aims to find all possible spectra for matrices whose $(i, j)$ -entry, for $i \neq = j$ , is nonzero precisely when $i$ is adjacent to $j$ . I…

math.SP2020

The Karpelevič Region Revisited

Stephen Kirkland, Thomas Laffey, Helena Smigoc

We consider the Karpelevič region $Θ_{n} \subset C$ consisting of all eigenvalues of all stochastic matrices of order $n$ . We provide an alternative characterisation of $Θ_n…

math.SP2019★ 3 cited

Completely positive factorizations associated with Euclidean distance matrices corresponding to an arithmetic progression

Damjana Kokol Bukovšek, Thomas Laffey, Helena Šmigoc

Euclidean distance matrices corresponding to an arithmetic progression have rich spectral and structural properties. We exploit those properties to develop completely positive fact…

math.CO2019

The strong spectral property for graphs

Jephian C. -H. Lin, Polona Oblak, Helena Šmigoc

We introduce the set $G^{SSP}$ of all simple graphs $G$ with the property that each symmetric matrix corresponding to a graph $G \in G^{SSP}$ has the st…

math.SP2018

A Nordhaus-Gaddum conjecture for the minimum number of distinct eigenvalues of a graph

Rupert H. Levene, Polona Oblak, Helena Šmigoc

We propose a Nordhaus-Gaddum conjecture for $q (G)$ , the minimum number of distinct eigenvalues of a symmetric matrix corresponding to a graph $G$ : for every graph $G$ excluding fou…

math.CA2016

Families of Newton-like inequalities for sets of self-conjugate complex numbers

Richard Ellard, Helena Šmigoc

We derive families of Newton-like inequalities involving the elementary symmetric functions of sets of self-conjugate complex numbers in the right half-plane. These are the first k…

math.RA2013★ 1 cited

Solution Theory for Systems of Bilinear Equations

Charles R. Johnson, Helena Šmigoc, Dian Yang

Bilinear systems of equations are defined, motivated and analyzed for solvability. Elementary structure is mentioned and it is shown that all solutions may be obtained as rank one…

math.SP2012

Power series with positive coefficients arising from the characteristic polynomials of positive matrices

Thomas J. Laffey, Raphael Loewy, Helena Šmigoc

Let A be an nxn (entrywise) positive matrix and let f(t)=det(I-t A). We prove that there always exists a positive integer N such that 1-f(t)^{1/N} has positive coefficients.