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December 22, 2014

December 22, 2014

Posted by **Sally** on Tuesday, February 17, 2009 at 7:09am.

-Find the eigenvalues and eigenvectors of P. And find a formula for P^n.

- math -
**Reiny**, Tuesday, February 17, 2009 at 8:51amIf I recall Markov's chain, the matrix for the above would be

.9 .1

.8 .2

Is this called the transition matrix ?

The steady state vector, or eigenvector, is found by multiplying an initial probability vector by that transition vector and then using that resulting vector in your next multiplication.

This will eventually converge to a fixed vector, that is

[a b] times

.9 .1

.8 .2 equals [a b]

then .9a + .1b = a

and .8a + .2b = b

also a + b = 1 by the laws of probability.

solving this I got [.5 .5]

hope this helps, haven't done this stuff in years. I think the last time I taught this was over 20 years ago.

- CORRECTION: math -
**Reiny**, Tuesday, February 17, 2009 at 9:30amI made a fundamental error in my matrix multiplication

my equations should have been

.9a + .8b = a

and .1a + .2b = b

[a b] should have been [8/9 1/9]

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