Share This Article:

Bounds for the Second Largest Eigenvalue of Real 3 × 3 Symmetric Matrices with Entries Symmetric about the Origin

Abstract Full-Text HTML XML Download Download as PDF (Size:104KB) PP. 606-609
DOI: 10.4236/am.2012.36094    3,525 Downloads   5,620 Views   Citations


Let ASn[a,b] denote a set of all real nxn symmetric matrices with entries in the interval [a,b]. In this article, we present bounds for the second largest eigenvalue λ2(A) of a real symmetric matrix A, such that AAS3 [-b,b].

Conflicts of Interest

The authors declare no conflicts of interest.

Cite this paper

B. Geoffrey, K. Benard and J. Akanga, "Bounds for the Second Largest Eigenvalue of Real 3 × 3 Symmetric Matrices with Entries Symmetric about the Origin," Applied Mathematics, Vol. 3 No. 6, 2012, pp. 606-609. doi: 10.4236/am.2012.36094.


[1] G. Constantine, “Lower Bounds for the Spectra of Symmetric Matrices with Nonnegative Entries,” Linear Algebra and its Applications, Vol. 65, 1985, pp. 171-178. doi:10.1016/0024-3795(85)90095-3
[2] R. Roth, “On the Eigenvectors Belonging to the Minimum Eigenvalue of an Essentially Nonnegative Symmetric Matrix with Bipartite Graph,” Linear Algebra and Its Applications, Vol. 118, 1989, pp. 1-10. doi:10.1016/0024-3795(89)90569-7.
[3] X. Zhan, “Extremal Eigenvalues of Real Symmetric Matrices with Entries in an Interval,” Siam Journal of Matrix Analysis and Applications, Vol. 27, No. 3, 2006, pp. 851-860. doi:10.1137/050627812
[4] J. Kopp, “Efficient Numerical Diagonalization of 3 × 3 Hermitian Matrices,” International Journal of Modern Physics C, Vol. 19, No. 3, 2008, pp. 523-548. doi:10.1142/S0129183108012303
[5] J. Brenner, “Hadamard Maximum Determinant Problem,” The American Mathematical Monthly, Vol. 79, No. 6, 1972, pp. 626-630.
[6] N. J. A Sloan and P. Simon, “The Encyclopaedia of Integer Sequences,” Academic Press Inc., London, 1995.

comments powered by Disqus

Copyright © 2020 by authors and Scientific Research Publishing Inc.

Creative Commons License

This work and the related PDF file are licensed under a Creative Commons Attribution 4.0 International License.