An eigenspace is not a special type of eigenvector; rather, it is the subspace formed by all eigenvectors associated with a specific eigenvalue. For instance, in the case of a rotation around the z-axis in ℝ3, the eigenvectors (0,0,1), (0,0,2), and (0,0,-1) all share the eigenvalue of 1. The eigenspace corresponding to this eigenvalue is represented by the z-axis. Understanding this distinction clarifies the relationship between eigenvectors and eigenspaces in linear algebra. This foundational concept is crucial for grasping more advanced topics in the field.