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We give a new proof for an equality of certain max-min and min-maxapproximation problems involving normal matrices. The previously publishedproofs of this equality apply tools from matrix theory, (analytic) optimizationtheory and constrained convex optimization. Our proof uses a classicalcharacterization theorem from approximation theory and thus exploits the linkbetween the two approximation problems with normal matrices on the one hand andapproximation problems on compact sets in the complex plane on the other.

Max-min and min-max approximation problems for normal matrices revisited