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)

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