Topic summary
Geometric multiplicity
Extracted from the Wikipedia article Eigenvalues and eigenvectors.
Matrix with repeated eigenvalues example
On the other hand, the geometric multiplicity of the eigenvalue 2 is only 1, because its eigenspace is spanned by just one vector [0 1 −1 1] and is therefore 1-dimensional. Similarly, the geometric multiplicity of the eigenvalue 3 is 1 because its eigenspace is spanned by just one vector [0 0 0 1]. The total geometric multiplicity γA is 2, which is the smallest it could be for a matrix with two distinct eigenvalues. Geometric multiplicities are defined in a later section.