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- W4380136241 abstract "Given a set $X$ of $ntimes n$ matrices and a positive integer $m$, we consider the problem of estimating the cardinalities of the product sets $A_1 dotsc A_m$, where $A_iin X$. When $X=mathcal M_n(mathbb{Z};H)$, the set of $ntimes n$ matrices with integer elements of size at most $H$, we give several bounds on the cardinalities of the product sets. Related to this result, we also give some bounds on the cardinalities of the set of solutions of the related equations such as $A_1 dotsc A_m=C$ and $A_1 dotsc A_m=B_1 dotsc B_m$. We also consider the case where $X$ is the subset of matrices in $mathcal M_n(mathbb{F})$, where $mathbb{F}$ is a field, with bounded rank $kleq n$. In this case, we completely classify the related product set." @default.
- W4380136241 created "2023-06-10" @default.
- W4380136241 creator A5074318431 @default.
- W4380136241 date "2023-06-07" @default.
- W4380136241 modified "2023-10-11" @default.
- W4380136241 title "Some counting questions for matrix products" @default.
- W4380136241 doi "https://doi.org/10.48550/arxiv.2306.04885" @default.
- W4380136241 hasPublicationYear "2023" @default.
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