Extracting a basis with fixed block inside a matrix

Pierre Youssef

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arXiv · 1401.6434

Extracting a basis with fixed block inside a matrix

Pierre Youssef

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Abstract

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 $V$.

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BibTeX RIS

Pierre Youssef. 2015-11-13. Extracting a basis with fixed block inside a matrix. https://arxiv.org/abs/1401.6434

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