Linear mapping/Eigenspace/Definition/Explanations/Remark

Thus we allow arbitrary values (not only eigenvalues) in the definition of an eigenspace. We will see in fact that they are linear subspaces. In particular, ${}0$ belongs to every eigenspace, though it is never an eigenvector. The linear subspace generated by an eigenvector is called an eigenline. For most (in fact all up to finitely many, in case the vector space has finite dimension) ${}\lambda$, the eigenspace is just the zero space.