When I see examples of getting the steady state vector with markov chains,
the sum of each column or row is usually one, but it isn't in my case. What do I do then?
If I have a $3\times 3$ matrix with the sum of 1 in the columns,
I would multiply the matrix with $x,y,z$ and get a linear system,
then I know that the columns add up to one,
so I set $x+y=1$, but what do I do in this case?
Transition matrix:
\begin{bmatrix}
0.8& 0 & 0\\
0 & 1.2 & 0\\
0 & 0 & 1
\end{bmatrix}
Best Answer
Your matrix is a diagonal matrix with an eigenvalue 1 of multiplicity 1 and eigenspace $\{\left( \begin{array}{c} 0\\ 0\\ z\\ \end{array} \right):z\in\mathbb{R}\}$. A steady state vector is an eigenvector with eigenvalue 1.