From qualitative matrices to quantitative restrictions
John S. Maybee, Gerry M. Wiener · Linear and Multilinear Algebra · 1988
We discuss one method of incorporating quantitative information into the theory of qualitative matrices. Our method consists of imposing conditions upon the principal minors of the matrix A which insure that their signs will be consistent with the signs of the diagonal elements (all assumed to be nonzero). A new diagonal dominance theorem is proved which gives sufficient conditions for such consistency. When the principal minors are consistent with the diagonal elements of A we show how to classify all elements of A and how to obtain precise sign information about many of the elements of A −1.