I've seen two definitions of generalized eigenvectors. One is $(A−λ⋅I)^kv=0$ and one where it is $Av = \lambda B v$. I get that they are the same thing but I'm curious. What is the point of both formulations and how does the first lead to the second?
Request for more info:
https://www.netlib.org/lapack/lug/node54.html
Thanks!