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A class of inverse \(M\)-matrices. (English) Zbl 0956.15012

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.

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
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