Mind Maps: How to Organize & Connect Your Ideas | Mural

8.2. Differential of a linear mapLet L: R^n -> R^m be a linear map. For any p ∈ R^n, there is a canonical identification Tp(R^n) ≅ R^n given by Φp(v) = (v1, ..., vn) where v = (v1, ..., vn) ∈ R^n. Show that the differential dLp : Tp(R^n) -> T(L(p))(R^m) is the map L: R^n -> R^m itself, with the identification of the tangent spaces as above.

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