A linear functional on a real vector space 
is a function 
, which satisfies the following properties.
1. 
,
and
2. 
.
When 
is a complex vector space, then 
is a linear map into the complex
numbers.
Generalized functions are a special case
of linear functionals, and have a rich theory surrounding them.
See also
Dual Vector Space,
Functional,
Generalized Function,
Linear
Function,
Vector Space
This entry contributed by Todd
Rowland
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Cite this as:
Rowland, Todd. "Linear Functional." From MathWorld--A Wolfram Web Resource, created by Eric
W. Weisstein. https://mathworld.wolfram.com/LinearFunctional.html
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