F. Sprung

A Log-Log Saving for Matrix-Algebra Length and Terseness

Let $\ell(\Mat_n(F))$ denote the length of the full matrix algebra for a field $F$, i.e. the largest of the least word length needed to span $\Mat_n(F)$, over all generating sets $S$ of $\Mat_n(F)$. \v{S}itov proved the general estimate $$ \ell(\Mat_n(F)) \leq 2n\log_2 n+4n-4. $$ The purpose of this paper is to obtain...