# Today I Learned

Some of the things I've learned every day since Oct 10, 2016

## 20: Generalized Eigenspaces

If $T$ is a linear operator on a finite-dimensional vector space $V$, and the characteristic polynomial of $T$ splits, then for a given eigenvalue $\lambda$ of $T$ with multiplicity $m$, the generalized eigenspace corresponding to $\lambda$ is

$K_{\lambda} = \textrm{ker} ((T - \lambda I)^m)$