In the process of finding the stationary distribution of a markov chain:
$\begin{pmatrix} \Pi _{1} & \Pi _{2} \end{pmatrix}\begin{pmatrix} P_{00} & P_{01}\\ P_{10}& P_{11} \end{pmatrix} =\begin{pmatrix} \Pi_{1} &\Pi_{2} \end{pmatrix}$
i.e $\boldsymbol{\pi} P = \boldsymbol{\pi}$, the stationary distribution is given by the left eigenvectors.
Why are row vectors used?
I am used to the column vector convention, and it's unclear to why this was broken in the resources I found on the stationary distribution. I'm assuming this is just because of how the probability matrix is defined. But why was the probability matrix defined in this way?