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