Past exam of the algebra, analysis and differential equations 1 course of the University of Oxford / 2013 / Algebra / 1 / a

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- Solution a

Solution

The dual space is the vector space of all linear functionals on

V

:

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

Addition and scalar multiplication are defined pointwise. The annihilator of a vector subspace is

U^{0} = {f \in V^{'} : f (u) = 0 for every u \in U} .

It is a vector subspace of

V^{'}

: linear combinations of functionals vanishing on

U

also vanish on

U

.

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