On inverse M-matrices
The author gives necessary and/or sufficient conditions for nonnegative square matrices to be inverse M-matrices, i.e. matrices of the form \(M=sI-B\) where \(B\geq 0\), \(\rho\) (B) is the spectral radius of B and \(s>\rho (B)\). Special cases where the matrices in consideration are also investigated; a square matrix A falls into the first category if \(A_ 1=PAP^ T\) is triangular for some permutation matrix P, and into the second if \(A=I+\alpha C\) where C is a (0,1)-matrix with zero main diagonal. The graph G(A) associated with the matrix A plays a key role in the author's investigations.
scientific article; zbMATH DE number 4101377