ELA, Volume 7, pp. 92-99, September 2000, abstract.
On Matrices with all Minors Negative
Shaun M. Fallat and P. van den Driessche
A matrix is called sign regular of order k if every minor of
order i has the same sign for each i=1,2,...,k. At one extreme
of the sign regular matrices lies the well studied and important
class of totally positive matrices. The purpose here is to
initiate a study of the other extreme of sign regular matrices,
namely the totally negative matrices (i.e., all minors negative).
Many aspects of this class are considered including: existence,
spectral properties, inverses, Schur complements, and
factorizations.