Abstract. 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 Minc. A constructive method is used everywhere, which can produce the realizing matrices explicitly.

AMS Subject Classification (1991): 15A18, 15A29, 15A48

Keyword(s): spectral list of a real or nonnegative matrix, local inverse eigenvalue problem, pseudo-metric generated by the matching distance

Received December 23, 2008, and in revised form April 7, 2009. (Registered under 83/2008.)