Local inverse spectrum theorems for real and nonnegative matrices - Förster Karl-Heinz (Acta scientiarum mathematicarum, 2010)
We prove several inverse spectrum theorems for real, nonnegative and positive matrices. The results are of a local character with respect to the topology generated by the matching distance of the spectral lists of matrices. We prove e.g. that the set of spectral lists of positive matrices is an open set in this topology, and extend a result of Mine. A constructive method is used everywhere, which can produce the realizing matrices explicitly.