The generalized eigenspace of a linear transformation 
on a finite-dimensional vector
space associated with an eigenvalue 
is 
for any sufficiently large 
, where 
is the identity map. One may
take 
equal to the dimension of the space. It is the direct
sum of the invariant subspaces corresponding to
all Jordan blocks belonging to 
.
Generalized Eigenspace
See also
Eigenvalue, Eigenspace, Generalized Eigenvector, Jordan Canonical FormExplore with Wolfram|Alpha
References
Axler, S. Linear Algebra Done Right, 3rd ed. Cham, Switzerland: Springer, 2015.Cite this as:
Weisstein, Eric W. "Generalized Eigenspace." From MathWorld--A Wolfram Resource. https://mathworld.wolfram.com/GeneralizedEigenspace.html