T. Laffey

collaborators

6 papers

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

The integer cp-rank of $2 \times 2$ matrices

Thomas Laffey, Helena Šmigoc

We show the cp-rank of an integer doubly nonnegative $2 \times 2$ matrix does not exceed $11$ .

math.SP2018

Diagonal realizability in the Nonnegative Inverse Eigenvalue Problem

Thomas J. Laffey, Helena Šmigoc

We show that if a list of nonzero complex numbers $σ = (λ_{1}, λ_{2}, \dots, λ_{k})$ is the nonzero spectrum of a diagonalizable nonnegative matrix, then $σ$ is the nonzero spectrum of a dia…

math.OC2018

Integer completely positive matrices of order two

Thomas Laffey, Helena Šmigoc

We show that every integer doubly nonnegative $2 \times 2$ matrix has an integer cp-factorization.

math.CO2017

The diagonalizable nonnegative inverse eigenvalue problem

Anthony G Cronin, Thomas J Laffey

In this paper we prove that the SNIEP $\neq =$ DNIEP, i.e. the symmetric and diagonalizable nonnegative inverse eigenvalue problems are different. We also show that the minimum $t > 0$ …

math.RA2015

On the Radius in Cayley-Dickson Algebras

Moshe Goldberg, Thomas J. Laffey

In the first two sections of this paper we provide a brief account of the Cayley-Dickson algebras and prove that the radius on these algebras is given by the Euclidean norm. With t…