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The spread of a matrix is defined as the maximum of distances between any twoeigenvalues of that matrix. In this paper we investigate spread maximization asa function on compact convex subset of the set of real symmetric matrices. Weprovide some general results and further, we study spread maximizing problem onthe set of symmetric matrices with entries restricted to the interval. Inparticular, we develop some results by X. Zhan, S. M. Fallat and J. J. Xing.

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