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arXiv · 1505.01893

Nonnegative rank depends on the field

Yaroslav Shitov
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Abstract

We present an example of a subfield $\mathcal{F}\subset\mathbb{R}$ and a matrix $A$ whose conventional and nonnegative ranks equal five, but the nonnegative rank with respect to $\mathcal{F}$ equals six. In other words, $A$ can be represented as a sum of five rank-one matrices with nonnegative real entries but not as a sum of five rank-one matrices with nonnegative entries in $\mathcal{F}$.

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Yaroslav Shitov. 2019-07-24. Nonnegative rank depends on the field. https://arxiv.org/abs/1505.01893

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