My question is: Given a matrix $A$ and its eigenvector $v$ which corresponds to $A$'s maximum eigenvalue, is there a closed form formula to calculate the derivative
where $u$ is an unrelated vector?
Please help! Thanks in advance!
I check matrix cookbook which shows
$$\partial v = (\lambda I-A)^\dagger\partial(A) v$$
where $\lambda$ is the corresponding eigenvalue, $\dagger$ is the symbol of pseudo-inverse. But I still don't know how to calculate the desired derivative.