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

Abstract

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 A∈AS3 [-b,b].