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arXiv · 1411.6234

A norm inequality for pairs of commuting positive semidefinite matrices

Koenraad M. R. Audenaert
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Abstract

For $k=1,\ldots,K$, let $A_k$ and $B_k$ be positive semidefinite matrices such that, for each $k$, $A_k$ commutes with $B_k$. We show that, for any unitarily invariant norm, \[ |||\sum_{k=1}^K A_kB_k||| \le ||| (\sum_{k=1}^K A_k)\;(\sum_{k=1}^K B_k)|||. \]

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Koenraad M. R. Audenaert. 2014-11-23. A norm inequality for pairs of commuting positive semidefinite matrices. https://arxiv.org/abs/1411.6234

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