Generalized eigenvalue problem ($Av=\lambda Bv$)

A generalized eigenvalue problem asks for a nonzero vector $v$ and scalar $\lambda$ satisfying $Av=\lambda Bv$. When $B$ is invertible, it is equivalent to the ordinary eigenvalue problem $B^{-1}Av=\lambda v$.

The generalized characteristic polynomial of a matrix pair $(A,B)$ is $\det (A-\lambda B)$. Every finite generalized eigenvalue is one of its roots.