Definition of geometric multiplicity of an eigenvalue

Created almost 9 years ago, updated about 8 hours ago

The geometric multiplicity of eigenvalue $\lambda$ is $\dim\ker(A-\lambda I)$. It counts independent eigenvectors for that eigenvalue and is between one and its algebraic multiplicity. For $\begin{bmatrix}1&1\\0&1\end{bmatrix}$, eigenvalue $1$ has geometric multiplicity one and algebraic multiplicity two.

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