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English(EN) A Counterexample to the Tang Zhang Schatten Norm Conjecture and Sharp Positive Results

Tang-Zhang Schatten范数猜想被反例证伪

作者 PulseAugur 编辑部 · [1 个来源] ·

研究人员通过一个反例证伪了Tang和Zhang关于Schatten范数的猜想，特别是关于矩阵不等式中全维度的最佳常数。他们使用两个明确的实数2x2秩一矩阵在p=3/2时证明，达到的比率超过了207/200，这与猜想的常数相矛盾。该论文还提供了肯定性结果，证明了当2 <= p < infinity时，秩最多为一的加数的猜想尖锐界限，并对等式情况进行了分类，以及p=infinity的终点陈述。此外，对于任意复数矩阵，对于m=2和p=4，已确立了猜想的尖锐常数。 AI

排序理由 在arXiv上发表的学术论文，提出了数学结果。[lever_c_demoted from research: ic=1 ai=0.1]

在 arXiv cs.LG 阅读 →

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Tang-Zhang Schatten范数猜想被反例证伪

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在arXiv上发表的学术论文，提出了数学结果。[lever_c_demoted from research: ic=1 ai=0.1]
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报道来源 [1]

  1. arXiv cs.LG TIER_1 English(EN) · Zijian Zeng, Houde Liu, Kurunathan Ratnavelu ·

    对唐张Schatten范数猜想的一个反例及尖锐的肯定性结果

    arXiv:2608.15558v1 Announce Type: cross Abstract: For $m\geq 2$, let $c_p(m)$ be the all-dimensional best constant in $$ \left\|\sum_{k=1}^m A_k\right\|_p \leq c_p(m)\left\|\sum_{k=1}^m |A_k|\right\|_p. $$ Tang and Zhang conjectured an explicit formula for every finite $p>1$. We …

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