Let $T : V \to V$ be an endomorphism. Why is $\dim \ker(T - \lambda \cdot I)$ the number of jordan block's correspoding to the eigenvalue $\lambda$?
2026-03-29 08:35:19.1774773319
Relation between $\dim\ker(T - \lambda I)$ and number of Jordan Block's
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Note that there is exactly one (linearly independent) eigenvector per Jordan block, and that $\dim \ker (T - \lambda I)$ is exactly the number of linearly independent eigenvectors.