## 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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