# Dimesnsion of an eigenspace

Note that a number may be a multiple root of the eigenvalue equation (for example, $\lambda^2- 2\lambda+ 1= (\lambda- 1)^2= 0$ has $\lambda= 1$ as a double root). That multiplicity is the "algebraic multiplicity". The algebraic multiplicity is always greater than or equal to the "geometric multiplicity", the number of independent eigenvectors corresponding to the eigenvalue, that Ackbeet refers to.