On the generalized nullspace of M-matrices and Z-matrices (Q1104377)

A preferred set for a matrix is an ordered set of vectors such that the image of each vector is a nonnegative linear combination of the subsequent ones. The coefficients in the linear combination depend on the graph structure of the matrix. The main goal of the paper is to reprove the preferred basis theorem for the generalized nullspace. The idea is originated from an early paper of the second author [Proc. Edinburgh math. Soc. Ser. 10, 108-122 (1956; Zbl 0074.254)], where the associated graph was supposed to be linearly ordered. The theorem is also extended from M-matrices to Z-matrices.