Eigenspace

The eigenspace of a square matrix <math>A</math> is the vector space spanned by all eigenvectors of a particular eigenvalue.

Stated another way, the kernel of the matrix <math>A-\lambda{I}</math> is called the eigenspace <math>E_\lambda</math> associated with <math>\lambda</math>. The dimension of the eigenspace is the geometric multiplicity of the corresponding eigenvalue.