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Name: Emily Johnson
Status: student
Age: 20s
Location: N/A
Country: N/A
Date: Around 1999

What is a dual space?

Suppose we have a collection of functions X = { f_1, f_2, f_3, . . . } We call this set a space because it has certain properties reminiscent of real space, if we regard each function as a ``point'' in this space.

Let a functional F on X be a widget that takes any function in the set (space) X and returns a number. Let a linear functional L on X be a functional which satisfies the following property:

F( a f_i + b f_j ) = a F (f_i) + b F (f_j)

for any f_i and f_j that are in X. a and b are unimportant numerical constants, like ``5'' or ``3.1415926535897932''.

The set of all linear functionals L on X constitute the dual space of X.


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