An energy decomposition theorem for matrices and related questions

Ali Mohammadi, Thang Pham, Yiting Wang

Given $A\subseteq G{L}_2({\mathbb{F}}_q)$, we prove that there exist disjoint subsets $B,C\subseteq A$ such that $A=B\bigsqcup C$ and their additive and multiplicative energies satisf…