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arXiv · 2607.11866

Counterexamples to a multivariable matrix Young conjecture

Zhekai Pang
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Abstract

We disprove Conjecture 5.1 of Lin concerning a multivariable extension of Ando's matrix Young inequality for positive semidefinite matrices. For every integer $m\geq4$, the conjectured eigenvalue inequality fails at the largest eigenvalue for $2\times2$ real rank-one orthogonal projections. We also give a $3\times3$ real positive semidefinite counterexample for $m=3$, where the failure occurs at the second eigenvalue.

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Zhekai Pang. 2026-06-20. Counterexamples to a multivariable matrix Young conjecture. https://arxiv.org/abs/2607.11866

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