[SOLVED] linear algebra determinant of linear operator 1. The problem statement, all variables and given/known data Let T be a linear operator on a finite-dimensional vector space V. Define the determinant of T as: det(T)=det([T]β) where β is any ordered basis for V. Prove that for any scalar λ and any ordered basis β for V that det(T - λIv) = det([T]β - λI). 2. Relevant equations Another part of the problem yielded that for any two ordered bases of V, β and γ , that det([T]β) = det([T]γ). 3. The attempt at a solution I need someone to help me understand the notation. I don't actually know what I am being asked to prove here.