Nonnegative matrices whose inverses are $M$-matrices
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- by Thomas L. Markham PDF
- Proc. Amer. Math. Soc. 36 (1972), 326-330 Request permission
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.References
- Miroslav Fiedler and Vlastimil Pták, On matrices with non-positive off-diagonal elements and positive principal minors, Czechoslovak Math. J. 12(87) (1962), 382–400 (English, with Russian summary). MR 142565
- F. Gantmakher and M. Krein, Sur les matrices complètement non négatives et oscillatoires, Compositio Math. 4 (1937), 445–476 (French). MR 1556987
- Thomas L. Markham, On oscillatory matrices, Linear Algebra Appl. 3 (1970), 143–156. MR 260769, DOI 10.1016/0024-3795(70)90010-8
Additional Information
- © Copyright 1972 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 36 (1972), 326-330
- MSC: Primary 15A48
- DOI: https://doi.org/10.1090/S0002-9939-1972-0309970-6
- MathSciNet review: 0309970