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

Author

Listed:
  • 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)

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.

Suggested Citation

  • Qianping Guo & Jinsong Leng & Houbiao Li & Carlo Cattani, 2019. "Some Bounds on Eigenvalues of the Hadamard Product and the Fan Product of Matrices," Mathematics, MDPI, vol. 7(2), pages 1-11, February.
    • Handle: RePEc:gam:jmathe:v:7:y:2019:i:2:p:147-:d:203380
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