Height bases, level bases, and the equality of the height and the level characteristics of anM-matrix
Daniel Hershkowitz, Hans Schneider · Linear and Multilinear Algebra · 1989
Let A be an M-matrix. We introduce the concepts of height basis, level basis, and height-level basis for the generalized nullspace of A. We explore the properties of such bases and of induced matrices. We use these results to prove some new conditions for the equality of the (spectral) height (Weyr) characteristic and the (graph theoretic) level characteristic of A, and to simplify proofs of known conditions. We also prove the existence of a Jordan basis for the generalized nullspace with all chains of maximal length nonnegative.