Is there a function i can use to calculate steady state?

Question

i was currently doing an excercise about steady state vector of a markov-chain, i was able to calculate it manually but I'm lost at how to calculate steady state using R, is there a function or library i can use to calculate this? any helps is appreciated, this is the transition matrix I'm using to calculate steady state:

P

P.data=c(0.95,0.03,0.05,0.97)
P = matrix(P.data, nrow=2,ncol=2,byrow=TRUE)
P

Answer 1

The steady state is a left eigen vector wit corresponding eigen value 1. To calculate the eigen vectors/values in R, there is the function eigen, but it calculates the right eigen vectors, so you have to transpose the Markov matrix.

> P.data <- c(0.95,0.03,0.05,0.97)
> P <- matrix(P.data, nrow=2, ncol=2, byrow=TRUE)
> eigen(t(P))
eigen() decomposition
$values
[1] 1.00 0.92

$vectors
           [,1]       [,2]
[1,] -0.7071068 -0.8574929
[2,] -0.7071068  0.5144958

The eigen vectors are defined up to a multiplicative factor, so here we find (0.5, 0.5) (the coefficients must sum to 1).

See this post and its answers for more details.