I have the following equation:
$$ R(x\otimes x)=x$$
Where $x\in \mathbb{R}^n$ is a nonnegativ vector ($x_i\geq0$) with $||x||_1=1 \quad$ ($\sum_1^n x_i=1$) and $R\in M_{n\times n^2}$ is a nonnegative matrix with $\sum_i R_{ij}=1$.
$\otimes$ stands for kronecker product
Is the solution unique?