Generalized eigenvector

A generalized eigenvector of a matrix A is a nonzero vector v, which has associated with it an eigenvalue λ having algebraic multiplicity k, satisfying

$(A-\lambda I)^{k}\mathbf {v} =\mathbf {0}$

Generalized eigenvectors can be used to determine the Jordan form.

See also

• eigenvector
• Jordan form