Let be a set of matrices over a field . We show that the -linear span of the words in of length at most
is the full -algebra generated by . This improves on the bound by Paz (1984) and an bound of Pappacena (1997).
"An improved bound for the lengths of matrix algebras." Algebra Number Theory 13 (6) 1501 - 1507, 2019. https://doi.org/10.2140/ant.2019.13.1501