  We devise achievable encoding schemes for distributed source compression for
computing inner products, symmetric matrix products, and more generally, square
matrix products, which are a class of nonlinear transformations. To that end,
our approach relies on devising nonlinear mappings of distributed sources,
which are then followed by the structured linear encoding scheme, introduced by
K\"orner and Marton. For different computation scenarios, we contrast our
findings on the achievable sum rate with the state of the art to demonstrate
the possible savings in compression rate. When the sources have special
correlation structures, it is possible to achieve unbounded gains, as
demonstrated by the analysis and numerical simulations.
