Inverse \(M\)-matrix inequalities and generalized ultrametric matrices
The authors introduce a class of matrices called generalized ultrametric matrices. That class is defined in terms of triangles in the weighted graph of the matrix, and it contains the ultrametric matrices as well as some unsymmetric matrices. The authors show that a generalized ultrametric matrix is the inverse of a row diagonally dominant \(M\)-matrix if and only if it contains no zero row and no two of its rows are identical. Inequalities and conditions for equality among the entries of the inverse of a row diagonally dominant \(M\)-matrix are also presented. Some of these inequalities and conditions for equality generalize results of Stieltjes on inverses of symmetric diagonally dominant \(M\)-matrices.
scientific article; zbMATH DE number 769032
scientific article