Abstract. We give an interpretation and a solution of the classical problem of the spectrum of the sum of Hermitian matrices in terms of stable bundles on the projective plane.Mathematics Subject Classification (1991). 14M25, 14F05.

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It is shown that, for any pair of cardinals with infinite sum, there exist a group and an equation over this group such that the first cardinal is the number of solutions to this equation and the second cardinal is the number of non-solutions to this equation. A countable torsion-free non-topologizable group is constructed.