Sign-nonsingular skew-symmetric matrices with the most nonzero entries (Q1923211)

This paper is a continuation of the author's work [ibid. 240, 207-229 (1996; Zbl 0851.15016)] in which he introduced and investigated the notion of a sign-nonsingular matrix \(A\) as a real one for which each matrix with the same sign pattern as \(A\) is nonsingular. In the presented paper the author shows that a sign-nonsingular skew-symmetric matrix of order \(2n\), \(n\geq 3\), has at most \(2(n^2+n-1)\) nonzero entries. The matrices for which the equality holds are characterized.