Geodesic
New bounds for the minimum eigenvalue of the Fan product of two $M$-matrices
Czechoslovak Mathematical Journal, Tome 64 (2014) no. 1, pp. 63-68.

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In this paper, we mainly use the properties of the minimum eigenvalue of the Fan product of $M$-matrices and Cauchy-Schwarz inequality, and propose some new bounds for the minimum eigenvalue of the Fan product of two $M$-matrices. These results involve the maximum absolute value of off-diagonal entries of each row. Hence, the lower bounds for the minimum eigenvalue are easily calculated in the practical examples. In theory, a comparison is given in this paper. Finally, to illustrate our results, a simple example is also considered.
DOI : 10.1007/s10587-014-0083-z
Classification : 15A18, 15A42, 15B48
Keywords: Fan product; minimum eigenvalue; $M$-matrix 
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     title = {New bounds for the minimum eigenvalue of the {Fan} product of two $M$-matrices},
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Cheng, Guanghui. New bounds for the minimum eigenvalue of the Fan product of two $M$-matrices. Czechoslovak Mathematical Journal, Tome 64 (2014) no. 1, pp. 63-68. doi : 10.1007/s10587-014-0083-z. http://geodesic.mathdoc.fr/articles/10.1007/s10587-014-0083-z/

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