Nabben, Reinhard A class of inverse \(M\)-matrices. (English) Zbl 0956.15012 Electron. J. Linear Algebra 7, 53-58 (2000). Nonnegative matrices whose inverses are \(M\)-matrices are called inverse \(M\)-matrices. It is still an open problem to characterize all inverse \(M\)-matrices. In this note a new class of inverse \(M\)-matrices is established. This class of nonsymmetric matrices generalizes the class of strictly ultrametic matrices. Section 2 contains the results. The class of inverse \(M\)-matrices is constructed in a similar way as the class of generalized ultrametric matrices. Reviewer: Yueh-er Kuo (Knoxville) Cited in 3 Documents MSC: 15B48 Positive matrices and their generalizations; cones of matrices 15B57 Hermitian, skew-Hermitian, and related matrices 15A09 Theory of matrix inversion and generalized inverses Keywords:nonnegative matrices; ultrametric matrices; inverse \(M\)-matrices PDFBibTeX XMLCite \textit{R. Nabben}, Electron. J. Linear Algebra 7, 53--58 (2000; Zbl 0956.15012) Full Text: DOI EuDML EMIS