Correct forward AD for linalg.eig and add checks (#70527)
Summary:
Pull Request resolved: https://github.com/pytorch/pytorch/pull/70527
This PR adds checks for the backward of `linalg.eig`, similar to those
deduced in https://github.com/pytorch/pytorch/pull/70253
It also modifies the function so that it does not save the input matrix,
as it's not necessary.
It also corrects the forward AD formula for it to be correct. Now all
the tests pass for `linalg.eig` and `linalg.eigvals`.
It also updates the docs to reflect better what's going on here.
cc jianyuh nikitaved pearu mruberry walterddr IvanYashchuk xwang233 Lezcano
Test Plan: Imported from OSS
Reviewed By: mruberry
Differential Revision: D33530148
Pulled By: albanD
fbshipit-source-id: 984521a04f81ecb28ac1c4402b0243c63dd6959d
