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Keywords:
Fan product; minimum eigenvalue; $M$-matrix
Fan product; minimum eigenvalue; $M$-matrix
Summary:
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.
References:
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[2] Fang, M. Z.: Bounds on eigenvalues of the Hadamard product and the Fan product of matrices. Linear Alegebra. Appl. 425 (2007), 7-15. DOI 10.1016/j.laa.2007.03.024 | MR 2334489 | Zbl 1128.15011
[3] Horn, R. A., Johnson, C. R.: Topics in Matrix Analysis. Cambridge University Press Cambridge (1991). MR 1091716 | Zbl 0729.15001
[4] Liu, Q. B., Chen, G. L.: On two inequalities for the Hadamard product and the Fan product of matrices. Linear Algebra Appl. 431 (2009), 974-984. MR 2535567 | Zbl 1183.15017
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