Peak characteristic and nonnegative signature

AbstractWe introduce the concepts of peak characteristic of an M-matrix A and of peak signature and nonnegative signature of subsets of the generalized nullspace E(A) of A, and we discuss the relations between them. We also study completions of sets to height bases and to level bases. Our results are then applied to the study of the nonnegativity of height bases for E(A). In particular, we show that a sequence can serve as the nonnegative signature of some height basis for E(A) if and only if it is less than or equal to the peak characteristic of A