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Algebraic and Geometric Multiplicity


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Let $ \lambda$ be an eigenvalue of matrix $ A$. The algebraic multiplicity $ m_{\lambda}$ of eigenvalue $ \lambda$ is defined as the multiplicity of $ \lambda$ as zero of $ \det(A - \lambda E_n)$.
The geometric multiplicity of eigenvalue $ \lambda$ is defined as the dimension $ d_{\lambda}$ of the eigenpace of $ \lambda$.

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[Examples]

  automatically generated 6/25/2018