MATLAB: Hellow, I have a problem To obtain participation factors, and specifically with the right and left eigenvectors in a paper I was reading about it, related in Power sistems, so Im tryin to use eig but the result are not the same: thank you 4uhelp

MATLABparticipation factors

>> A
A =
[ a, b] [ 0, d]
>> [D V W]=eig(A)
D =
[ 1, -b/(a – d)] [ 0, 1]
V =
[ a, 0] [ 0, d]
W =
     1     2
>>

Best Answer

Hi,
The eigenvalues and right-side eigenvectors are correct, they are just returned in a different order than you assume:
>> syms a b d
>> A = [a b; 0 d]
A =
[ a, b]
[ 0, d]
>> [V, D, P] = eig(A)
V =
[ 1, -b/(a - d)]
[ 0,          1]
D =
[ a, 0]
[ 0, d]
P =
     1     2
The column vectors of V are r1 and r2 from the paper, just with a different scaling for r2.
The problem with the third output is that for regular MATLAB matrices, this would be the left-side eigenvectors of the matrix. However, for symbolic matrices, it's a vector of indices to the linearly independent eigenvectors (see here )
To get the left eigenvalues of A, simply compute the right eigenvectors of A transposed:
>> [W, D] = eig(A.')
W =
[ (a - d)/b, 0]
[         1, 1]
D =
[ a, 0]
[ 0, d]
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