Take the 2-minute tour ×
Mathematics Stack Exchange is a question and answer site for people studying math at any level and professionals in related fields. It's 100% free, no registration required.

I have got the following transition matrix:

$$A = \begin{pmatrix} p & 1-p \\ 1-q & q \end{pmatrix}$$

How can one use the jordan normal form to get a closed-form to calculate such a values $$A^n_{i,j}$$ ?

share|improve this question
1  
Did you try to compute the powers of a matrix in jordan normal form? What did you find? –  Rasmus Jul 4 '12 at 12:19

1 Answer 1

You find $P$ and $B$ such that $B$ is in Jordan form and $A=PBP^{-1}$. Then you find a formula for $A^n$ involving $B^n$, and take the advice of Rasmus from the comments.

share|improve this answer
    
I'll try. Thanks! –  Heinrich Jul 4 '12 at 12:59

Your Answer

 
discard

By posting your answer, you agree to the privacy policy and terms of service.

Not the answer you're looking for? Browse other questions tagged or ask your own question.