Thank you very much for the existence of this post :)
Regarding your last paragraph
"It turns out that A-1 has the same eigenvectors as A; its eigenvalues are λ-1 of the original’s"
it turns out that I can't get the same result. This is what Matlab gives me:
>> A
A =
2.0000 1.0000
1.5000 2.0000
>> [x,l]=eig(A)
x =
0.6325 -0.6325
0.7746 0.7746
l =
3.2247 0
0 0.7753
>> [x_i,l_i]=eig(inv(A))
x_i =
0.6325 0.6325
-0.7746 0.7746
l_i =
1.2899 0
0 0.3101
What seems to be the problem?
Thanks again,
Emerson