(adsbygoogle = window.adsbygoogle || []).push({}); 1. The problem statement, all variables and given/known data

The Markov matrix A = [.9 .3; .1 .7] has eigenvalues 1 and .6, and the power method u_{k}=A^{k}u_{0}converges to [.75 .25]^{T}. Find the eigenvectors of A^{-1}. What does the inverse power method u_{-k}=A^{-1}u_{0}converge to (after you multiply by .6^{k})?

2. Relevant equations

3. The attempt at a solution

Eigenvalue 1 is the dominant one when using the power method on A. However, we're interested in the smallest eigenvalue when dealing with the inverse power method, in this case .6. The eigenvalues of A^{-1}are:

(1/.6) and 1. According to theory, the eigenvectors of A^{-1}are the same as those in A.

So, the corresponding eigenvector to the value .6 is [-1 1]^{T}.

From there, I'm simply stumped. Can anyone please help?!

1. The problem statement, all variables and given/known data

2. Relevant equations

3. The attempt at a solution

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# Inverse Power Method and Eigenvectors

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