Path product and inverse M-matrices
Yan Zhu, Chengyi Zhang, Jun Liu · Electronic Journal of Linear Algebra · 2011
It is known that inverse M-matrices are strict path product (SPP) matrices, and that the converse is not true for matrices of order greater than 3.In this paper, given a normalized SPP-matrix A, some new values s ′ for which A + s ′ I is an inverse M-matrix are obtained.Our values s ′ extend the values s given by Johnson and Smith [C.R. Johnson and R.L. Smith.Positive, path product, and inverse M-matrices.Linear Algebra Appl., 421: 328-337, 2007.].The question whether or not a 4 × 4 SPP-matrix is a P-matrix is settled.