I face the following problem. I generate a big $1202 \times 1202$ stochastic matrix $Q$ whose columns adds to $1$ (up to numeric precision). The elements of $Q$ are in $[0,1]$. I use the eigendecomposition
[ R, D ] = eig( Q )
and I compute
L = inv( R )
I have NO warning that R is close to singular and the elements of R may have big imaginary parts.
(I tried to use [ R, D, L ] = eig( Q )but R*L dose not provide an identity matrix).
I get a result where:
Q ~= real( R*D*L )
At the end I have better results in matlab just by using
Q^200000 than R*D^200000*L.
Is there any explanation for this behavior?