Dual (English)
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Definition (undergraduate level)
- Let V be a vector space over F . The dual of V , written V* , is the set of all linear maps f : V → F . The operations of addition and scalar multiplication are defined in the obvious pointwise manner.
- The dual of a set is the set of continuous linear maps f : E → C . Note that f is continuous iff it is bounded. Such maps are therefore bounded linear functionals.
- The dual of a set is the set of continuous linear maps f : E → C . Note that f is continuous iff it is bounded. Such maps are therefore bounded linear functionals.
Relations
- broader:
- (en) Bijection
- references:
- (en) Functional
- (en) Vector space
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