# Why transformations in quantum mechanics are linear?

In quantum mechanics, when we want to introduce reference frame change, we do it such that $\left|\psi'\right> = U\left|\psi\right>$. Using the fact that $\left<\psi|\psi\right>=1$, we then deduce that $U$ should be unitary.

My question is, how do we know that the transformation is a linear operator? Is this a postulate of quantum physics? Is it completely general?