multiplicity of eigenvalue

Suppose $V$ is a finite dimensional vector space over a field $𝔽$, and suppose $L:V\to V$ is a linear map. Suppose also that $\lambda \in 𝔽$ is an eigenvalue of $L$, that is, $\det (L-\lambda I)=0$.

The algebraic multiplicity, denoted by $A_{\lambda }(L)$, of $\lambda$ is the multiplicity of the root $\lambda$ to the polynomial $\det (L-\lambda I)=0$. The geometric multiplicity of $\lambda$, denoted by $G_{\lambda }(L)$, is the dimension of $\ker (L-\lambda I)$, the eigenspace of $\lambda$.

Title	multiplicity of eigenvalue
Canonical name	MultiplicityOfEigenvalue
Date of creation	2013-03-22 15:15:15
Last modified on	2013-03-22 15:15:15
Owner	matte (1858)
Last modified by	matte (1858)
Numerical id	5
Author	matte (1858)
Entry type	Definition
Classification	msc 15A18
Defines	geometric multiplicity
Defines	algebraic multiplicity