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Intervals of certain classes of Z-matrices

100%
Kannan M., Sivakumar K.
Discussiones Mathematicae - General Algebra and Applications
|
2014
|
tom 34
|
nr 1
85-93
EN
Let A and B be M-matrices satisfying A ≤ B and J = [A,B] be the set of all matrices C such that A ≤ C ≤ B, where the order is component wise. It is rather well known that if A is an M-matrix and B is an invertible M-matrix and A ≤ B, then aA + bB is an invertible M-matrix for all a,b > 0. In this article, we present an elementary proof of a stronger version of this result and study corresponding results for certain other classes as well.
2
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Some new bounds of the minimum eigenvalue for the Hadamard product of anM-matrix and an inverseM-matrix

100%
Zhao J., Sang C.
Open Mathematics
|
2016
|
tom 14
|
nr 1
81-88
EN
Some convergent sequences of the lower bounds of the minimum eigenvalue for the Hadamard product of a nonsingular M-matrix B and the inverse of a nonsingular M-matrix A are given by using Brauer’s theorem. It is proved that these sequences are monotone increasing, and numerical examples are given to show that these sequences could reach the true value of the minimum eigenvalue in some cases. These results in this paper improve some known results.
3
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New bounds for the minimum eigenvalue ofM-matrices

100%
Wang F., Sun D.
Open Mathematics
|
2016
|
tom 14
|
nr 1
1007-1013
EN
Some new bounds for the minimum eigenvalue of M-matrices are obtained. These inequalities improve existing results, and the estimating formulas are easier to calculate since they only depend on the entries of matrices. Finally, some examples are also given to show that the bounds are better than some previous results.
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