Linear algebra: Kenneth Hoffman
Section 3.4
Exercise
- 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} $ .