Let $al $ be a $p imes q$ interval matrix with $p geq q$ and with the endpoints of all its entries in $Q$. We prove that, if $al $ contains a rank-$r$ real matrix with $r in {2, q-2,q-1,q}$, then it contains a rank-$r$ rational matrix.
Interval matrices: realization of ranks by rational matrices / Elena Rubei. - In: LINEAR ALGEBRA AND ITS APPLICATIONS. - ISSN 0024-3795. - STAMPA. - 608:(2021), pp. 299-321. [10.1016/j.laa.2020.09.017]
Interval matrices: realization of ranks by rational matrices
Elena Rubei
2021
Abstract
Let $al $ be a $p imes q$ interval matrix with $p geq q$ and with the endpoints of all its entries in $Q$. We prove that, if $al $ 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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