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.