I'm currently working in game theory, and have the following equilibrium $\begin{bmatrix}1&0&1\end{bmatrix}$. I'd like to show the trivial equilibrium which results from this is given by the following dyadic product:
$$\begin{bmatrix} 1 & 0 & 1\\ \end{bmatrix} \otimes \begin{bmatrix} 0 & 1 & 0\\ \end{bmatrix}$$
Which I've computed to be:
$$\begin{bmatrix} 0 & 1 & 0\\ 0 & 0 &0\\ 0&1&0 \end{bmatrix}$$
For my research, it's enough to show this computation is correct for it to be a trivial equilibrium. Is this computation correct?
Understanding the dyadic product is given by the following:
$$\begin{matrix} [a & b & c] \end{matrix} \otimes \begin{matrix} [d & e & f]\\ \end{matrix} = \begin{matrix} ad & ae & af\\ bd & be & bf\\ cd & ce & cf \end{matrix}$$
The computation of the given dyadic product is correct.