 Solution

ID: past-exam-of-the-linear-algebra-course-of-the-university-of-oxford/2017/2/a/i/solution

V^{'} = Hom_{F} (V, F),

(ϕ + ψ) (v) = ϕ (v) + ψ (v), (a ϕ) (v) = a ϕ (v) .

Given the basis

e_{1}, \dots, e_{n}

, its dual basis consists of the coordinate linear functionals

f_{i} (j = 1 \sum n a_{j} e_{j}) = a_{i}, f_{i} (e_{j}) = δ_{ij} .

In particular,

dim V^{'} = dim V = n

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