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Mathematics 2019, 7(2), 147; https://doi.org/10.3390/math7020147

Some Bounds on Eigenvalues of the Hadamard Product and the Fan Product of Matrices

1
Department of Mathematics and Information Science, Henan University of Finance and Economics, Zhengzhou 450046, China
2
School of Mathematical Sciences, University of Electronic Science and Technology of China, Chengdu 611731, China
3
Engineering School, DEIM, University of Tuscia, 01100 Viterbo, Italy
*
Authors to whom correspondence should be addressed.
Received: 14 November 2018 / Revised: 21 January 2019 / Accepted: 31 January 2019 / Published: 3 February 2019
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Abstract

In this paper, an upper bound on the spectral radius ρ ( A B ) for the Hadamard product of two nonnegative matrices (A and B) and the minimum eigenvalue τ ( C D ) of the Fan product of two M-matrices (C and D) are researched. These bounds complement some corresponding results on the simple type bounds. In addition, a new lower bound on the minimum eigenvalue of the Fan product of several M-matrices is also presented. These results and numerical examples show that the new bounds improve some existing results. View Full-Text
Keywords: Hadamard product; nonnegative matrices; spectral radius; fan product; M-matrix; inverse M-matrix; minimum eigenvalue Hadamard product; nonnegative matrices; spectral radius; fan product; M-matrix; inverse M-matrix; minimum eigenvalue
This is an open access article distributed under the Creative Commons Attribution License which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited (CC BY 4.0).
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Guo, Q.; Leng, J.; Li, H.; Cattani, C. Some Bounds on Eigenvalues of the Hadamard Product and the Fan Product of Matrices. Mathematics 2019, 7, 147.

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