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Given a matrix, $P$, why does finding its eigenvalues, say they are $\{\lambda_1, \lambda_2\}$ then the general form of $p_{ij}^{(n)}=A_{ij}\lambda_1^n+B_{ij}\lambda_2^n$? Thanks.

Added: Context: $P$ is a transition matrix

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    Sorry, but a question about $p_{ij}^{(n)}$ what is it? element of the matrix $P^n$? And what are $A$ and $B$ some numbers right?2011-10-12
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    @maximus: You are right on both. :)2011-10-12
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    No indexes like $i$ and $j$ in the $p_{ij}^{(n)}$ formula? So every element of the matrix has the same value?2011-10-12
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    @maximus: Edited2011-10-12

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