The Algebric Multiplicity and Geometric Multiplicity
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Mathematics/Linear Algebra
The MultiplicityDefintion 1. Let $T \in \mathcal{L}(V)$, and let $\lambda$ be an eigenvalue of $T$ with characteristic polynomial $f(t)$. Then (a) The algebric multiplicity of $\lambda$ is the largest positive integer $k$ for which $(t - \lambda)^k$ is a factor of $f(t)$.(b) The geometric multiplicity of $\lambda$ is $\dim(E_{\lambda})$ where $E_{\lambda}$ is the eigenspace of T corresponding to..