Kyungpook Mathematical Journal

Department of Mathematics, Kyungpook National University (경북대학교 자연과학대학 수학과)
권호 표지
DOI QR코드

DOI QR Code

New Bounds for the Numerical Radius of a Matrix in Terms of Its Entries

  • Received : 2020.03.18
  • Accepted : 2021.02.08
  • Published : 2021.09.30
Download PDF
⟨ Previous Next ⟩

Abstract

In this work we give new upper and lower bounds for the numerical radius of a complex square matrix A using the entries and the trace of A.

Keywords

Acknowledgement

The author would like to thank the reviewers for their very helpful comments and suggestions.

References

  1. M. Goldberg, E. Tadmor and G. Zwas, The numerical radius and spectral matrices, Linear and Multilinear Algebra, 2(1975), 317-326. https://doi.org/10.1080/03081087508817075
  2. R. Horn and C. R. Johnson, Topics in Matrix Analysis, Cambridge University Press, Cambridge, 1991.
  3. C. R. Johnson, A gersgorin inclusion set for the field of values of a finite matrix, Proceedings of the american mathematical society. 41(1973), 57-60. https://doi.org/10.1090/S0002-9939-1973-0318191-3
  4. J. K. Merikoski and R. Kumar, Lower bounds for the numerical radius, Linear Algebra Appl., 410(2005), 135-142. https://doi.org/10.1016/j.laa.2005.02.029
  5. R. A. Smith and L. Mirsky, The areal spread of matrices, Linear Algebra Appl., 2(1969), 127-129. https://doi.org/10.1016/0024-3795(69)90021-4