Concrete minimal 3 × 3 Hermitian matrices and some general cases

Abstract

Given a Hermitian matrix M ∈ M3(ℂ) we describe explicitly the real diagonal matrices DM such that ║M + DM║ ≤ ║M + D║ for all real diagonal matrices D ∈ M3(ℂ), where ║ · ║ denotes the operator norm. Moreover, we generalize our techniques to some n × n cases.

Keywords

• Minimal Hermitian matrix
• diagonal matrix
• quotient operator norm
• best approximation
• 15A12
• 15A60
• 15A83
• 15B57
• 41A35