Positivity of principal minors, sign symmetry and stability.
The authors study the relation between positivity of principal minors, sign symmetry and stability of matrices. In Section 1 they give many definitions of terminologies used in this paper. In Section 2 they show that for sign symmetric matrices positivity of principal minors and stability are equivalent. In Section 3, for \(3\times 3\) matrices they generalize the results of the previous section. This result does not hold in general for matrices of any oder \(n\). In Section 4 they study matrices whose scalings have \(P_0\)-matrix square. In Section 5 they consider the relation between the spectra of \(P^S\)-matrices and \(Q^S\)-matrices. Finally, they refer to the relation between \(P^S\)-matrices or \(Q^S\)-matrices and stability, concentrating on \(P^2\)-matrices. They give many open questions.
scientific article; zbMATH DE number 1903580
scientific article