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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

 

Nonnegative matrices whose inverses are $ M$-matrices


Author: Thomas L. Markham
Journal: Proc. Amer. Math. Soc. 36 (1972), 326-330
MSC: Primary 15A48
MathSciNet review: 0309970
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Abstract: A characterization of a class of totally nonnegative matrices whose inverses are M-matrices is given. It is then shown that if A is nonnegative of order n and $ {A^{ - 1}}$ is an M-matrix, then the almost principal minors of A of all orders are nonnegative.


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DOI: http://dx.doi.org/10.1090/S0002-9939-1972-0309970-6
PII: S 0002-9939(1972)0309970-6
Keywords: Nonnegative matrix, totally nonnegative matrix, M-matrix, almost principal minor
Article copyright: © Copyright 1972 American Mathematical Society