A Sharp Upper-Bound for the Norm of Positive Semi-Definite Block Matrices

SOUTHEAST ASIAN BULLETIN OF MATHEMATICS（2022）

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摘要

This paper studies the positive semi-definite 2x2 block matrix M = X* B E C2nx2n. A new sharp upper bound for IIMII is provided under the condition of X being normal, for any unitarily invariant norm IImiddotII. A special pattern among the eigen-values of M when A + B = kI, for some k > 0, is explored.

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关键词

Positive semi-definite matrix, Block matrix, Unitarily invariant norm

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