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October 29th, 2013, 07:09 PM   #1
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Steady state vector for the Markov Matrix

I have to find the steady state vector for matrix is M= [.5 .8
.5 .2]

Would the vector [.8
.5]
be in the steady state because [.5 .8
.5 .2] times x = x so the system reduces down to -.5x+.8y=0 ?
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October 30th, 2013, 01:20 PM   #2
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Re: Steady state vector for the Markov Matrix

Quote:
Originally Posted by 84grandmarquis
I have to find the steady state vector for matrix is M= [.5 .8
.5 .2]

Would the vector [.8
.5]
be in the steady state because [.5 .8
.5 .2] times x = x so the system reduces down to -.5x+.8y=0 ?
You are correct. However
Quote:
so the system reduces down to -.5x+.8y=0
is confusing - what are x and y? You said x = vector (.8,.5).
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October 31st, 2013, 11:48 AM   #3
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Re: Steady state vector for the Markov Matrix

Don't use "x" to represent a vector and then to represent one of the components of the vector!
Yes, if is a "steady state vector" for this matrix, we must have


which gives .5x+ .8y= x, .5x+ .2y= y

-.5x+ .8y= 0, .5x- .8y= 0. Those are just multiples of each other so as long as , it is a steady state vector.
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