I was trying to understand the basic ideas of the operator-stable distributions. I found the papers by [Hudson](https://ac.els-cdn.com/0047259X80900792/1-s2.0-0047259X80900792-main.pdf?_tid=2953aa8d-c0a2-4a76-91f6-3f41bfdf0994&acdnat=1533563860_f86a125d48c19655037145541942ca02) and [Sato](https://ac.els-cdn.com/0047259X87900911/1-s2.0-0047259X87900911-main.pdf?_tid=6317fe1b-4153-4d73-b9c5-a8e36fdb790d&acdnat=1533564079_c9c2ff34136b6d94052444a56e4adcbf). However, unfortunately, I am being unable to understand the mathematical expressions, the authors have used, to define the same. So, to make the definition understandable, I wrote: 

>If $X_1 \stackrel{D}{=} X_2 \stackrel{D}{=} X$, then $X$ is operator-stable if there exists a real matrix $C$ and a vector $d$ such that $AX_1 + BX_2 \stackrel{D}{=} CX$, where $A$, and $B$ are real, square matrices and $X_1$, $X_2$, and $X$ are real vectors.

Have I understood right (only for simple scenarios)? Also, I have not found any examples (like Gaussian, Cauchy etc.) of the operator-stable distributions. Some examples will be really helpful. If there are no such examples available in closed form, then can I find the density numerically at a given point?