# Eigenvalue with ranks

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• Apr 26th 2008, 12:54 PM
tttcomrader
Eigenvalue with ranks
Let T be a linear operator on a finite dimensional vector space V. Let $\lambda$ be an eigenvalue of T. Prove that if $rank((T - \lambda I )^m = rank ((T - \lambda I ) ^{m+1} )$ for some integer m, then $K_{ \lambda } = N ((N- \lambda I)^m$