Geometric multiplicity
, the dimension of the eigenspace of the eigenvalue ; always .
Definition 4.7 (Geometric Multiplicity)
The geometric multiplicity of an eigenvalue , or , is the dimension of its eigenspace , i.e. the maximum number of linearly independent eigenvectors corresponding to .
Statement
Proposition 4.8
Consider an matrix, and an eigenvalue of . Then
Related
Stated in
- Definition 4.7 (Geometric Multiplicity)§4.2 Eigenspaces and Multiplicity
- Proposition 4.8§4.2 Eigenspaces and Multiplicity