Algebraic and Geometric Multiplicity
The algebraic multiplicity of an eigenvalue $\lambda_0$ is the number of factors $(x - \lambda_0)$ in the Characteristic Equation of the matrix.
The geometric multiplicity of the eigenvalue is the Dimension of the eigenspace $E_{\lambda_0}$.
It is always true that $1 \leq g.m.(\lambda_0) \leq a.m.(\lambda_0)$