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I have a question about computing the following linear algebraic operation

Suppose

$u = (1, 0, 0)$

$v = \begin{pmatrix} 1\\ 0\\ 0\end{pmatrix}$

$A = \begin{pmatrix} 0.5 &0.2 &0.3\\0.2 &0.3 &0.5\\ 0.3 &0.5 &0.2\end{pmatrix}$

and

$g(n) = u\cdot A^n\cdot v$

I want to calculate

$g(20)/g(19)$ constructing a Markov process and using Metropolis algorithm.

1 Answers 1