SLn Equivariant Matrix-Valued Valuations on Polytopes

All $\textrm{SL}(n)$ equivariant matrix-valued valuations on polytopes in $\mathbb{R}^{n}$ are completely classified without any continuity assumptions. Moreover, the symmetry assumption of matrices is removed. The moment matrix is shown to be the only such valuation if $n\geq 4$, while new functionals show up in dimensions two and three.