On constructions of partially nonpositive matrices
A square matrix is called partially non-positive if each of its principal minors is non-positive. Various properties of partially non-positive matrices related to the problem if the matrix is or can be transformed into a negative matrix are derived, e.g., it is shown that if A is a partially non-positive matrix and all off-diagonal elements are non-zero, then there is a diagonal matrix S with \(+1\) or -1 in the diagonal such that SAS is negative.
scientific article; zbMATH DE number 4083826