6 citations · 14 across the 14 of their papers we have counts for
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A note on Guo's perturbation result for symmetric nonnegative matrices
Helena Šmigoc
In 1997 Guo Wuwen proved that if is the spectrum of a nonnegative matrix with Perron eigenvalue and real, then is…
Stochastic Matrices Realising the Boundary of the Karpelevi\v c Region
Stephen Kirkland, Helena Šmigoc
A celebrated result of Karpelevi\v c describes the collection of all eigenvalues arising from the stochastic matrices of order The boundary of consists of roots o…
The Karpelevič Region Revisited
Stephen Kirkland, Thomas Laffey, Helena Smigoc
We consider the Karpelevič region consisting of all eigenvalues of all stochastic matrices of order . We provide an alternative characterisation of $Θ_n…
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…
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 , the minimum number of distinct eigenvalues of a symmetric matrix corresponding to a graph : for every graph excluding fou…
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.