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arXiv · 1409.3020

Linear spanning sets for matrix spaces

Giacomo Micheli·Joachim Rosenthal·Paolo Vettori
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Abstract

Necessary and sufficient conditions are given on matrices $A$, $B$ and $S$, having entries in some field $\mathbb F$ and suitable dimensions, such that the linear span of the terms $A^iSB^j$ over $\mathbb F$ is equal to the whole matrix space. This result is then used to determine the cardinality of subsets of $\mathbb F[A]S\mathbb F[B]$ when $\mathbb F$ is a finite field.

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Giacomo Micheli, Joachim Rosenthal, Paolo Vettori. 2014-09-10. Linear spanning sets for matrix spaces. https://doi.org/10.1016/j.laa.2015.06.008

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