This paper is concerned with bounds of eigenvalues of a complex matrix. Both lower and upper bounds of modulus of eigenvalues are given by the Stein equation. Furthermore, two sequences are presented which converge to the minimal and the maximal modulus of eigenvalues, respectively. We have to point out that the two sequences are not recommendable for practical use for finding the minimal and the maximal modulus of eigenvalues.

eigenvalues, lower and upper bounds, Stein equation

65F10, 65F15

- G.\, D. Hu, G.\ and D. Hu: A relation between the weighted logarithmic norm of matrix and Lyapunov equation. BIT} {\mi 40 CrossRef
- G.\, D. Hu, M.\ and Z. Liu: The weighted logarithmic matrix norm and bounds of the matrix exponential. Linear Algebra Appl.} {\mi 390 CrossRef
- T.\, H. Huang, R.\ and S. Ran: A simple estimation for the spectral radius of block H-matrics. J. Comput. Appl. Math.} {\mi 177 CrossRef
- B. Mond, J.\ and E. Pecaric: On an inequality for spectral radius. Linear and Multilinear Algebra} {\mi 20 CrossRef
- Q. Zhu, G.\, D. Hu, and L. Zeng: Estimating the spectral radius of a real matrix by discrete Lyapunov equation. J. Difference Equations Appl. CrossRef