Talk:Generalized eigenvector/Archive 1

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Archive 1

Generalized eigenvalue problem

Doesn't this relate to generalized eigenvalues that satisfy the modified characteristic equation $\det(\mathbf {A} -\lambda \mathbf {B} )=0$ for matrices $\mathbf {B}$ not limited to the identiy matrix as in normal eigen-systems? — Preceding unsigned comment added by 90.184.23.22 (talk) 05:45, 25 April 2008 (UTC)

"Generalized" is a word that is overused in mathematics. What you referring to is called the "Generalized Eigenvalue Problem". In that case, it is the "problem" that has been generalized, while for this page, it is the meaning of "eigenvector" that has been generalized. One difference: the generalization of "eigenvector" does not also generalize "eigenvalue" - the eigenvalue for any generalized eigenvector also has ordinary eigenvectors associated with it (in particular,

(A - λI) k -1 v

). Eigenguy (talk) 01:28, 12 July 2012 (UTC)