Extensions of Perron–Frobenius splittings and relationships with nonnegative Moore–Penrose inverses
Agrawal N. Sushama, K. Premakumari, K. C. Sivakumar · Linear and Multilinear Algebra · 2013
An -matrix has the form , where and is eventually nonnegative, i.e. is entry wise nonnegative for all sufficiently large integers . In this article, two new types of splittings of matrices are introduced. The class of matrices possessing a splitting of one of these types includes -matrices as a subclass. The authors derived necessary and sufficient conditions for the convergence of these splittings in terms of an extended notion of the nonnegativity of the Moore–Penrose inverse. The work reported here widens the applicability of the existing results.