矩阵内固定块基的提取
Extracting a basis with fixed block inside a matrix
摘要：
给定$U$一个秩为$n$的$n\times m$矩阵和$U$内部的列的$V$块，我们考虑提取秩为$n$的列的块的问题，该块最小化逆的Hilbert-Schmidt范数，同时保持块$V$。这推广了Gluskin-Olevskii的先前结果，并且当给定“好”块$V$时改进了估计。
英文摘要：
Given $U$ an $n\times m$ matrix of rank $n$ and $V$ block of columns inside $U$, we consider the problem of extracting a block of columns of rank $n$ which minimize the Hilbert-Schmidt norm of the inverse while preserving the block $V$. This generalizes a previous result of Gluskin-Olevskii, and improves the estimates when given a "good" block $V$.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
