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

Qianping Guo, Jinsong Leng, Houbiao Li and Carlo Cattani
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Qianping Guo: Department of Mathematics and Information Science, Henan University of Finance and Economics, Zhengzhou 450046, China
Jinsong Leng: School of Mathematical Sciences, University of Electronic Science and Technology of China, Chengdu 611731, China
Houbiao Li: School of Mathematical Sciences, University of Electronic Science and Technology of China, Chengdu 611731, China
Carlo Cattani: Engineering School, DEIM, University of Tuscia, 01100 Viterbo, Italy

Mathematics, 2019, vol. 7, issue 2, 1-11

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.

Keywords: Hadamard product; nonnegative matrices; spectral radius; fan product; M -matrix; inverse M -matrix; minimum eigenvalue (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2019
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