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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