On single and double Soules matrices (Q2497242)

As defined by \textit{G. W. Soules} [Linear Multilinear Algebra 13, 241--251 (1983; Zbl 0516.15013)], a Soules basis matrix of a sign pattern \(N\) is an orthogonal matrix \(R \in \mathbb{R}^{n \times n}\) (generated in a certain way by a positive vector) with the property that for any nonnegative diagonal matrix \(\Lambda\) with decreasing entries, the symmetric matrix \(A = R \Lambda R\) has nonnegative entries. In the paper under review, the concept of a pair of double Soules basis matrices of sign pattern \(N\) is introduced.