Let $J=\begin{pmatrix}2&1&0&0&0&0\\0&2&0&0&0&0\\0&0&2&1&0&0\\0&0&0&2&0&0\\0&0&0&0&3&1\\0&0&0&0&0&3\end{pmatrix}$. Find geometric multiplicity of eigenvalue 2 (integer).
There are two Jordan blocks associated with eigenvalue 2, each of size two. Each contributes one independent eigenvector, so nullity of J−2I and geometric multiplicity are **2**.
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