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Inequalities for monotonic pairs of \(Z\)-matrices. (English) Zbl 0907.15015

The authors extend a result of Ky Fan to show that if \(A, B\) are \(K_0\) or \(N_0\) matrices with \(A\leq B\) entrywise then linear combinations \(aA+bB\) are respectively \(K_0,N_0\) matrices, and show related inequalities.

MSC:

15A45 Miscellaneous inequalities involving matrices
15B48 Positive matrices and their generalizations; cones of matrices
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References:

[1] Berman A., Non-negative matrices in the mathematical sciences (1979)
[2] Fan Ky, Proc. Koninkl. Ned. Akad. Wetenschap. Ser. 67 pp 602– (1964)
[3] Fiedler M., Czech. Math. J. 12 pp 382– (1962)
[4] DOI: 10.1016/0024-3795(82)90108-2 · Zbl 0501.15011 · doi:10.1016/0024-3795(82)90108-2
[5] DOI: 10.1080/03081089008817978 · Zbl 0694.15006 · doi:10.1080/03081089008817978
[6] DOI: 10.1080/03081089108818066 · Zbl 0726.15012 · doi:10.1080/03081089108818066
[7] DOI: 10.1016/0024-3795(86)90269-7 · doi:10.1016/0024-3795(86)90269-7
[8] DOI: 10.1016/0024-3795(87)90166-2 · Zbl 0615.15007 · doi:10.1016/0024-3795(87)90166-2
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