  We prove that every entire self-shrinking solution on $\mathbb{C}^n$ to the
K\"{a}hler-Ricci flow with strictly real convex potential must be quadratic.
The very same argument also gives a pointwise proof for the rigidity of entire
self-shrinking solutions to Lagrangian mean curvature flow in pseudo-Euclidean
space obtained by Q. Ding and Y.L. Xin. Furthermore, we show that our argument
works for a larger class of equations.
