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Tang-Zhang Schatten Norm Conjecture Disproven with Counterexample

By PulseAugur Editorial · [1 sources] ·

Researchers have disproven a conjecture by Tang and Zhang regarding the Schatten norm, specifically the all-dimensional best constant in a matrix inequality. Using two explicit real 2x2 rank-one matrices at p=3/2, they demonstrated that the attained ratio exceeds 207/200, contradicting the conjectured constant. The paper also provides positive results, proving the conjectured sharp bound for rank-at-most-one summands when 2 <= p < infinity and classifying equality cases, along with the endpoint statement for p=infinity. Additionally, for arbitrary complex matrices, the conjectured sharp constant is established for m=2 and p=4. AI

RANK_REASON Academic paper published on arXiv presenting mathematical results. [lever_c_demoted from research: ic=1 ai=0.1]

Read on arXiv cs.LG →

AI-generated summary · Google Gemini · from 1 sources. How we write summaries →

Tang-Zhang Schatten Norm Conjecture Disproven with Counterexample

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Academic paper published on arXiv presenting mathematical results. [lever_c_demoted from research: ic=1 ai=0.1]
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COVERAGE [1]

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

    A Counterexample to the Tang Zhang Schatten Norm Conjecture and Sharp Positive Results

    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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