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3. let v be a vector space over a eld f...

Question: let v be a vector space over a eld f...

Question details

Let V be a vector space over a ﬁeld F. Let T : V→V be a linear map. Let W be a subspace of V. We say W is T-invariant if for every w ∈ W, we have T(w) ∈ W. Let W be T-invariant. Then T restricts to a linear map W→W, which we denote by TW (given by TW(w) = T(w)). Let V/W be the quotient of V by W （linear aglebra）