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arXiv · 1407.0331

Positivity of Partitioned Hermitian Matrices with Unitarily Invariant Norms

Chi-Kwong Li·Fuzhen Zhang
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Abstract

We give a short proof of a recent result of Drury on the positivity of a $3\times 3$ matrix of the form $(\|R_i^*R_j\|_{\rm tr})_{1 \le i, j \le 3}$ for any rectangular complex (or real) matrices $R_1, R_2, R_3$ so that the multiplication $R_i^*R_j$ is compatible for all $i, j$, where $\|\cdot\|_{\rm tr}$ denotes the trace norm. We then give a complete analysis of the problem when the trace norm is replaced by other unitarily invariant norms.

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Chi-Kwong Li, Fuzhen Zhang. 2014-08-22. Positivity of Partitioned Hermitian Matrices with Unitarily Invariant Norms. https://arxiv.org/abs/1407.0331

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