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

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.