ABSTRACT
As was observed in (6.16) already, the study of a vector space endomorphism T: V → V can be substantially simplified if V can be decomposed into a direct sum of T-invariant subspaces, say V = ⊕ i V i , because then we only need to study the restrictions T|v i : V i → V i (which is easier because the spaces V i are smaller than the original space V). The smallest invariant subspaces we can possibly find are those of dimension one. Now a one-dimensional T-invariant subspace of a K-vector space V has the form K · V where v ∈ V \ {0} and where Tv = λv for some λ ∈ K. Thus we give the following definition.
