geometric multiplicity

The dimension of an eigenvalue's eigenspace — how many independent eigenvectors it actually supplies.

The geometric multiplicity of an eigenvalue $\lambda$ is $\dim(\operatorname{Nul}(A-\lambda I))$ , the dimension of its eigenspace. It always satisfies $1\le(\text{geometric multiplicity})\le(\text{algebraic multiplicity})$ . When the two agree for every eigenvalue, $A$ is diagonalizable; when geometric multiplicity falls short, $\lambda$ is defective.