ELA, Volume 12, pp. 17-24, January 2005, abstract.
Positive Entries of Stable Matrices
Shmuel Friedland, Daniel Hershkowitz, and
Siegfried M. Rump
The question of how many elements of a real
positive stable matrix must be positive is
investigated. It is shown that any real stable
matrix of order greater than 1 has at least two
positive entries. Furthermore, for every stable
spectrum of cardinality greater than 1 there
exists a real matrix with that spectrum with
exactly two positive elements, where all other
elements of the matrix can be chosen to be negative.