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Given a Hermitian matrix M ∈ M 3 (ℂ) we describe explicitly the real diagonal matrices D M  such that ║M + DM║ ≤ ║M + D║ for all real diagonal matrices D ∈ M 3 (ℂ), where ║ · ║ denotes the operator norm. Moreover, we generalize our techniques to some n × n cases.

Concrete minimal 3 × 3 Hermitian matrices and some general cases