27th Conference of the International Linear Algebra Society (ILAS 2026)

Session

Eigenvalues of Nonnegative and Stochastic Matrices

MS 20

May 20, 2026, 10:45 AM

74. C-realizability in the Symmetric Nonnegative Inverse Eigenvalue Problem: a combinatorial characterization

Julio Moro (Universidad Carlos III de Madrid)

5/20/26, 10:45 AM

Eigenvalues of Nonnegative and Stochastic Matrices

Minisymposium Talk

The Real Nonnegative Inverse Eigenvalue problem (hereforth, RNIEP) consists, for a given positive integer n, in characterizing the lists of n real numbers which are the spectrum of some n × n matrix with real entries. C-realizability was originally introduced in [1] as a sufficient condition for the RNIEP. It was shown back then that C-realizability included as particular cases most of the...

219. Characteristic Polynomials of Nonnegative Hessenberg Matrices

Helena Šmigoc (University College Dublin)

5/20/26, 11:10 AM

Eigenvalues of Nonnegative and Stochastic Matrices

Minisymposium Talk

The nonnegative inverse eigenvalue problem (NIEP) seeks to characterize the multisets of complex numbers that can be realized as the spectra of nonnegative matrices. Hessenberg matrices have been used in several central constructive results within this field, including the resolution of the NIEP for $4 \times 4$ matrices, the characterization of spectra where all non-Perron eigenvalues possess...

509. NIEP: positive and irreducible realizations

Miriam Pisonero (Universidad de Valladolid, Spain)

5/20/26, 11:35 AM

Eigenvalues of Nonnegative and Stochastic Matrices

Minisymposium Talk

The Nonnegative Inverse Eigenvalue Problem (NIEP) is the problem of characterizing the lists $\sigma$ of $n$ complex numbers (counting multiplicities) that are the spectrum of a nonnegative matrix of size $n$. A list $\sigma$ is said to be realizable if there exists a nonnegative matrix whose spectrum is $\sigma$.

Another way of facing the NIEP is to focus the attention on the...

236. New Results on the Doubly Stochastic Inverse Eigenvalue Problem

Ludovick Bouthat (Université Laval)

5/21/26, 11:00 AM

Eigenvalues of Nonnegative and Stochastic Matrices

Minisymposium Talk

Stochastic matrices are matrices with nonnegative entries whose rows each sum to $1$. When a matrix and its transpose are both stochastic, it is said to be \emph{doubly stochastic}. In 1938, Kolmogorov proposed the problem of characterizing the region of possible eigenvalues of an $n \times n$ stochastic matrix, and Karpelevich gave a complete description thirteen years later. This talk...

61. Eigenvalue regions and realising matrices for monotone stochastic matrices

Brando Vagenende (Department Business Technology and Operations, Data Analytics Laboratory, Vrije Universiteit Brussel (VUB))

5/21/26, 11:25 AM

Eigenvalues of Nonnegative and Stochastic Matrices

Minisymposium Talk

This talk presents spectral properties of monotone stochastic matrices which are characterised by the fact that each row stochastically dominates the preceding one, and which arise in contexts such as intergenerational mobility, equal-input models, and credit-rating systems.

In analogy with the stochastic matrices, for the monotone stochastic matrices both the individual eigenvalues as the...

49. Spectrally Complete Subsets and Eigenvalue Regions of classes of Stochastic Matrices

Brecht Verbeken (Vrije Universiteit Brussel)

5/21/26, 11:50 AM

Eigenvalues of Nonnegative and Stochastic Matrices

Minisymposium Talk

Karpelevich’s theorem describes the single-eigenvalue region
$ \Theta_n=\{\lambda\in{\bf C}:\lambda\in\sigma(A)\ {\rm for\ some\ }A\in{\bf R}^{n\times n} \ {\rm row\mbox{-}stochastic}\}. $
The set of row-stochastic matrices is the polytope $\mathrm{conv}(V_n)$, where $V_n$ consists of the $n^n$
deterministic Markov kernels ($0$-$1$ matrices with exactly one $1$ in each row).
For a...