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Let , n S a b denote a set of all real nxn symmetric matrices with entries in the interval A , a b . In this article, we present bounds for the second largest eigenvalue 2 A of a real symmetric matrix A, such that . 3 , S bb A Adoi:10.4236/am.2012.36094 fatcat:z473i44q5faqnledxewpxj6zjm