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pezola
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[SOLVED] linear algebra determinant of linear operator
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).
Another part of the problem yielded that for any two ordered bases of V, β and γ , that det([T]β) = det([T]γ).
I need someone to help me understand the notation. I don't actually know what I am being asked to prove here.
Homework Statement
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).
Homework 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).
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.