This tag is for questions relating to Generalized-eigenvector, a vector which satisfies certain criteria which are more relaxed than those for an (ordinary) eigenvector.

Definition: If $A$ is an $n × n$ matrix, a generalized eigenvector of $A$ corresponding to the eigenvalue $λ$ is a nonzero vector $\mathbf X$ satisfying $$(A − λI)^p ~\mathbf X = \mathbf 0$$ for some positive integer $p$.

Equivalently, it is a nonzero element of the nullspace of $~(A − λI)^p~.$

  • A regular eigenvector is a generalized eigenvector of order $1$.
  • Every $n × n$ matrix $A$ has $n$ linearly independent generalized eigenvectors associated with it.

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