Today I Learned

Some of the things I've learned every day since Oct 10, 2016

23: Dual Spaces

A linear functional is a mapping f: V \rightarrow F from a vector space V to its field F.

V ^*, the dual space of V, is the vector space of all such linear functionals, with addition of functionals and multiplication by scalars from F being defined in the expected manner.

If V is finite-dimensional, then \textrm{dim}(V ^*) = \textrm{dim}(V) and V ^* is isomorphic to V, but this is not the case when V is infinite-dimensional.

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