1. The problem statement, all variables and given/known data 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 a and b for V such that a = [T]b? Prove that such bases exist if and only if there is an invertible linear operator U on V such that T = USU-1. (Outline of proof: If a = [T]b, let U be the operator which carries a onto b and show that S = UTU-1. Conversely, if T = USU-1 for some invertible U, let a be any ordered basis for V and let b be its image under U. Then show that a = [T]b. where [T]b means T with relative to b 3. The attempt at a solution I'm not sure where to start. Is there a particular theorem to use here?