I have a matrix $R$. Now I want to verify that $R$ maps $D$ to $C$, in the sense that $x^+ = Rx^-$, where $x^-$ is a element from $D = \{x \in R^2 | Jx \geq 0 \vee Jx \leq 0\}$ and $x^+$ a element from $C = \{x \in R^2 | Ex \geq 0 \vee Ex \leq 0\}$, herein
$$ R = \begin{bmatrix} 0.6 & 0 \\ 0.25 & 0 \end{bmatrix},\ J = \begin{bmatrix} 1 & -2 \\ 0.1 & 1 \end{bmatrix},\ E = \begin{bmatrix} 1 & -2 \\ -0.1 & 1 \end{bmatrix} $$
How do I verify/compute this?
$R$ has only rank $1$, so every image vector is a multiple of $v=\begin{pmatrix}0.6\\0.25\end{pmatrix}$. Since $Ev =\begin{pmatrix}0.1\\0.19\end{pmatrix}\ge 0$,any multiple of it is $\ge 0$ or $\le 0$.