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arXiv · 2604.24087

Submatrices with the best-bounded inverses: an asymptotically tight upper bound for $\mathbb{C}^{n \times 2}$

Yuri Nesterenko
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Abstract

The long-standing hypothesis formulated by Goreinov, Tyrtyshnikov and Zamarashkin \cite{GTZ1997} has recently been solved affirmatively in the case of real two-column matrices by Sengupta and Pautov \cite{SP2026}. In this paper, we consider the complex variant of this problem and prove the asymptotically tight upper bound for spectral norms of the best-bounded inverse $2 \times 2$ submatrices of an arbitrary complex $n \times 2$ matrix with orthonormal columns.

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Yuri Nesterenko. 2026-04-27. Submatrices with the best-bounded inverses: an asymptotically tight upper bound for $\mathbb{C}^{n \times 2}$. https://arxiv.org/abs/2604.24087

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