Exact overlaps for "all" integrable matrix product states of rational spin chains

The overlaps between integrable matrix product states (MPS) and Bethe states are important in both the non-equilibrium statistical physics and the AdS/CFT duality. We present the general MPS overlap formula. The result is a product of a ratio of Gaudin determinants and a prefactor. The Gaudin determinants depend on the spin chain but not on the MPS. The MPS dependent prefactor is given for all integrable MPS of the $\mathfrak{gl}_{N}$, $\mathfrak{o}_{N}$ and $\mathfrak{sp}_{N}$ symmetric spin chains with arbitrary representations.