This is a question for someone familiar with random walks and its connection to eigenvalues.
So we have $M=D\cdot{A_G}$ in which $A_G$ is the adjacency matrix and $D$ is the diagonal, where $(D)_{ii}=1/d(i).$
In what I am reading, I have written here that "$M^{T}\pi=1.\pi$ expresses the fact that $\pi$ is the stationary distribution."
I am unsure on how to prove that $M^T$ satisifies this eigenvalue equation? Is it basic knowledge from matrices? $\pi$ is left eigenvalue and $1$ is right eigenvalue. $M^T$ is simply $M$ after time $T$ for our random walk.
Here is what I am reading http://www.cs.elte.hu/~lovasz/erdos.pdf.
See page 3 and 4 for intro definitions.
See page 14 for where my problem has arose, it is where section 3 starts.
Thank you for any help you can offer, please let me know if you require more info.