Structure properties of W matrices
Let M be a real \(n\times n\) matrix. For any subset \(\alpha\) \(\subseteq \{1,...,n\}\), let M(\(\alpha)\) denote the matrix obtained from the identity matrix by replacing the columns indexed by the elements of \(\alpha\) by the corresponding columns of -M. Let \({\hat \alpha}\) denote the complement of \(\alpha\) in \(\{\) 1,...,n\(\}\). Then the authors call M a W-matrix if the cones generated by the columns of M(\(\alpha)\) and M(\({\hat \alpha}\)), respectively, intersect in 0 for every subset \(\alpha\) [cf. the authors, ibid. 87, 243-256 (1987; Zbl 0611.90093)]. The present paper deals with further properties of these matrices.
scientific article; zbMATH DE number 4077456