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# The dimension of a eigenspace is less than or equal to the (algebraic) multiplicity of the eigenvalue.

Put content here**Theorem:** The dimension of an eigenspace $E_\lambda$ is less than or equal to the algebraic multiplicity of $\lambda$. That is, geometric multiplicity $\leq$ algebraic multiplicity. Equality holds iff the matrix is diagonalizable.

# Parents

* Eigenvalues and eigenvectors