Generalized \(P_ 0\)- and \(Z\)-matrices
The study of linear complementarity problems often relies on the structure of the associated matrix. The same can be expected of the generalized problem. In this paper, the authors characterize the vertical block \(P_ 0\)- and \(Z\)-matrix classes. These characterizations include extensions of some of the classical results of \textit{M. Fiedler} and \textit{V. Pták} [Czechosl. Math. J. 12(87), 382-400 (1962; Zbl 0131.248); Numer. Math. 9, 163-172 (1966; Zbl 0148.258)] for the square \(P_ 0\)- and \(Z\)-matrices. The choice of these two matrix classes relates to their potential to further advance the application areas of linear algebra. The paper is organized as follows. In Section 2, the authors give definitions and notation needed for the development. Sections 3 and 4 are devoted to mathematical properties and characterizations of the \(Z\) and \(P_ 0\) classes, respectively. Section 5 is a brief conclusion.
scientific article; zbMATH DE number 519695
scientific article