ELA, Volume 13, pp. 90-110, March 2005, abstract.

Spectral Properties of Sign Symmetric Matrices


Daniel Hershkowitz and Nathan Keller

Spectral properties of sign symmetric matrices are 
studied. A criterion for sign symmetry of shifted 
basic circulant permutation matrices is proven, and 
is then used to answer the question which complex 
numbers can serve as eigenvalues of sign symmetric
3-by-3 matrices. The results are applied in the 
discussion of the eigenvalues of QM-matrices. In 
particular, it is shown that for every positive 
integer n there exists a QM-matrix A such that A^k 
is a sign symmetric P-matrix for all k at most n, but
not all the eigenvalues of A are positive real numbers.