Mathematica has this command "Eigensystem[{m,a}]", which (to quote their documentation) "gives the generalized eigenvalues and eigenvectors of m with respect to a." I have never encountered this concept before, ever - that there can be eigenvectors of matrices(adsbygoogle = window.adsbygoogle || []).push({}); with respect toother 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.

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# Generalized eigenvectors/eigenvalues

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