 A generalized eigenvalue problem (second sense) is the problem of finding a vector that obeys

where and are matrices.If obeys this equation, with some , then we call the "generalized eigenvector" of and (in the second sense), and is called the "generalized eigenvalue" of and (in the second sense) which corresponds to the generalized eigenvector .The possible values of must obey the following equation

In the case we can find linearly independent vectors so that for every , , where then we define the matrices and such that

Then the following equality holds

And the proof is

And since is invertible, we multiply the equation from the right by its inverse, finishing the proof.