5. Generalized Inverse-Positivity
Society for Industrial and Applied Mathematics eBooks · 1994
1 INTRODUCTION Let K be a proper cone, i.e., a closed, pointed, convex subset of . A matrix is called K-monotone if it satisfies Ax∈K→x∈K. 1.1 This is equivalent to A being nonsingular and A−1 ∈π (K) ,i.e., A−1 K⊆K. 1.2 We call matrices satisfying (1.2), K-inverse-positive. An example of K-monotone matrices is matrices of the form where B ∊ π(K) and . Such matrices, which are called K-nonsingular M-matrices, are of particular interest and will be studied in detail in Chapter 6 for .