Vorträge im Schwerpunkt Reelle Geometrie und Algebra
Freitag, 22. Oktober 2010, um 14:15 Uhr
in D522
(Oberseminar, O'Shea)
Anthony Cronin
(Dublin)
The Nonnegative Inverse
Eigenvalue Problem
Abstract:
The nonnegative inverse eigenvalue problem (NIEP) is the
problem of determining a set of necessary and sufficient conditions
such that the list
σ= (λ1,λ2,..., λn)
of complex numbers is the spectrum of a nonnegative n×n matrix A. We call such
an A,
a realizing
matrix for σ and say that σ is realized by A. While this
problem has attracted a lot of attention in the last 50 years it
remains unsolved for any n≥
5. We will give a brief history of the problem and
motivations for its solution, as well as a survey of related problems.
Of related interest is the allowable perturbations one can make on a
realizable list while preserving realizabilty. We will outline some
recent developments to this end.
Reference
P. D. Egleston, T. D. Lenker, S. K. Narayan. The nonnegative inverse
eigenvalue problem, Linear Algebra and its Applications, 379: 475-490,
2004.
zuletzt
geändert am 13. Oktober 2010
