- #1
James2012
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Homework Statement
I'm having a problem with a question. I need to find the transition matrix in the form
T=UAU^-1
where U=[V1 V2]
Homework Equations
T=UAU^-1
where U=[V1 V2]
The Attempt at a Solution
my original transition matrix is [0.9 0.002; 0.1 0.998]
from that i calculated the eigenvalues to be 0.898 and 1
which means A=[0.898 0;0 1]
i found the eigenvectors to be V1=[1;-1] and V2=[0.002;0.1]
subbing these into the equation above i end up with the original transition matrix, however the question says to make use of the result [0.02 0.707;0.9998 -0.707]^-1 = [0.9823 0.9823;1.3866 -0.0278]
which means they use different eigenvectors, but I am not sure how they got that