2023/03/13 by Yuri Valentinovich Nesterenko, Nesterenko, Yuri
Computer Science · Mathematics · Engineering · #Matrix Theory and Algorithms #Graph theory and applications #graph theory and CDMA systems
paper · pdf · doi:10.48550/arxiv.2303.07492
The following hypothesis was put forward by Goreinov, Tyrtyshnikov and Zamarashkin in \citeGTZ1997. For arbitrary real n × k matrix with orthonormal columns a sufficiently "good" k × k submatrix exists. "Good" in the sense of having a bounded spectral norm of its inverse. The hypothesis says that for arbitrary k = 1, …, n-1 the upper bound can be set at √(n). Supported by numerical experiments, the problem remained open for all non-trivial cases (1 < k < n-1). In this paper we will give the proof for the simplest of them (n = 4, k = 2).