Mathematics-Online lexicon: Algebraic and Geometric Multiplicity

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	Mathematics-Online lexicon:
	Algebraic and Geometric Multiplicity

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Let $\lambda$ be an eigenvalue of matrix

. 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 $\lambda$ .

Example:

Example: Algebraic and Geometric Multiplicity

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automatically generated 6/25/2018