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

Question:
What is a dual space?

Replies:
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.

NEWTON is an electronic community for Science, Math, and Computer Science K-12 Educators, sponsored and operated by Argonne National Laboratory's Educational Programs, Andrew Skipor, Ph.D., Head of Educational Programs.