Linear Functional (original) (raw)
Algebra Applied Mathematics Calculus and Analysis Discrete Mathematics Foundations of Mathematics Geometry History and Terminology Number Theory Probability and Statistics Recreational Mathematics Topology
Alphabetical Index New in MathWorld
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
Explore with Wolfram|Alpha
Cite this as:
Rowland, Todd. "Linear Functional." From MathWorld--A Wolfram Web Resource, created by Eric W. Weisstein. https://mathworld.wolfram.com/LinearFunctional.html