Note on the spread of real symmetric matrices with entries in fixed interval

The spread of a matrix is defined as the maximum distances between any two eigenvalues that matrix. In this paper we investigate maximization function on compact convex subset set real symmetric matrices. We provide some general results and further study maximizing problem Sn[a,b] (the matrices with entries restricted to interval [a,b]). particular develop by X. Zhan (see [13]), S. M. Fallat J. Xing [3]).