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Some new lower bounds for the minimum eigenvalue of the Hadamard product of an M-matrix and its inverse

Yaotang Li, Xin Liu, Xiaoying Yang, Chaoqian Li
2011 The Electronic Journal of Linear Algebra  

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For the Hadamard product A • A −1 of an M -matrix A and its inverse A −1 , some new lower bounds for the minimum eigenvalue of A • A −1 are given. These bounds improve the results of [H.B. Li, T.Z. Huang, S.Q. Shen, and H. Li. Lower bounds for the minimum eigenvalue of Hadamard product of an M -matrix and its inverse. Linear Algebra Appl., 420:235-247, 2007] and [Y.T. Li, F.B. Chen, and D.F. Wang. New lower bounds on eigenvalue of the Hadamard product of an M -matrix and its inverse.
more » ... .technion.ac.il/iic/ela Proof. By Lemma 2.1 (a) and Lemma 2.2 (a), we have From T ji = min{m ji , n ji }, we get b ji ≤ T ji b ii , i, j ∈ N, i = j.
doi:10.13001/1081-3810.1463 fatcat:t2y5tsvttjgz3h3t7mafuimhge
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Yaotang Li, Xin Liu, Xiaoying Yang, Chaoqian Li. "Some new lower bounds for the minimum eigenvalue of the Hadamard product of an M-matrix and its inverse." The Electronic Journal of Linear Algebra (2011)