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

Barini Geoffrey, Kivunge Benard, Jotham Akanga

Department of Pure and Applied Mathematics, Jomo Kenyatta University of Agriculture and Technology, Nairobi, Kenya.
Department of Pure and Applied Mathematics, Kenya Polytechnic University College, Nairobi, Kenya.

DOI: 10.4236/am.2012.36094                

Abstract

Let A_Sn[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 A∈A_S3 [-b,b].

Keywords

Bounds; Determinant; Eigenvalues; Trace

Conflicts of Interest

The authors declare no conflicts of interest.

References

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