UnivMathComp/200806

Section 3.4

Exercise

1. Let $ V $ be a finite-dimensional vector space over the field $ F $ and let $ S $ and $ T $ be linear operators on $ V $ . We ask: When do there exist ordered bases $ B $ and $ B’ $ for $ V $ such that $ [S]_B=[T]_{B’} $ ?

(proof)

We want to show that $ [S]_B=[T]_{B’} $ ⇔ ∃invertible linear operator $ U $ such that $ T=USU^{-1} $ .