On Positive Principal Minors

The relation between matrices with all principal minors positive and positive definite matrices is explored in the non-symmetric case. It is shown that simple rescaling of rows and columns is insufficient to transform the former into the latter. As a consequence it appears that the class of problems that can be solved by complementary pivot theory of mathematical programming has been non-trivially extended beyond the convex case represented by linear and quadratic programming and takes its place along with another important extension of Lemke and Howson for the matrix associated with bi-matrix games. (Author).