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.