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arXiv · 1911.05762

Interval matrices: realization of ranks by rational matrices

Elena Rubei
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Abstract

Let $α$ be a $p \times q$ interval matrix with $p \geq q$ and with the endpoints of all its entries in the set of the rational numbers. We prove that, if $α$ contains a rank-$r$ real matrix with $r \in \{2, q-2,q-1,q\}$, then it contains a rank-$r$ rational matrix.

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Elena Rubei. 2024-12-01. Interval matrices: realization of ranks by rational matrices. https://doi.org/10.1016/j.laa.2020.09.01

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