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**with respect to**other matrices. All I have ever come across is that [itex]\lambda[/itex] is a generalized eigenvalue of [itex]A[/itex] with generalized eigenvector [itex]\vec x[/itex] if there exists some [itex]p \in \mathbb N[/itex] such that [itex](A-\lambda I)^p\vec x = 0[/itex].

Can someone please explain what it *means* to be a "generalized eigenvalue or eigenvector" of m with respect to a? Maybe it is related to the concept I mentioned above, but if so, I don't see it.