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Mathematics-Online lexicon:

Generalized Eigenvector, Generalized Eigenspace

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Let $ \lambda$ be an eigenvalue of matrix $ A$ with algebraic multiplicity $ m$. A vector $ v$ with

$\displaystyle (A-\lambda E)^mv=0\,,\quad v\neq 0

is called generalised eigenvector for eigenvalue $ \lambda$. All generalised eigenvectors together with the zero vector form a subspace of dimension $ m$ called generalised eigenspace $ H_\lambda$ for eigenvalue $ \lambda$. This subspace is invariant under the linear mapping $ A$.

  automatically generated 5/17/2011