Markov chains - from vs. to in transition matrix?

Question

So I thought that the rows represent the "from" state and the columns represent the "to" state. But here, it looks to be the opposite: (Source)

Wouldn't it actually be that 10% of D transition to R and that 20% of R transition to D? Or am I getting this confused myself?

Answer 1

You are right, normally the rows count for the "from" state and the columns count for the "to" state. But, you can transpose the matrix and keep all the other ideas the same, keeping in mind the vectors should be transposed as well, and that the multiplication should be from the other side.

For example if $P$ is your markov matrix, and $\pi$ is a stationary vector, instead of writing $\pi P$ you write $P^t \pi^t$.