In terms of the dual space, it is quite evident why dimensions add.

In particular, their dual space is trivial, that is, it contains only the zero functional.

The dual space carries the action of G given by .

With this norm, the dual space is also a Banach space.

Thus the topological dual space contains only the zero functional.

Consequently, the dual space is an important concept in the study of functional analysis.

The algebraic dual space is defined for all vector spaces.

They form a basis for the dual space of V, called the dual basis.

In the dual space, it expresses the creation of the economic values associated with the outputs from set input unit prices.

So we only need to know how to assign "numbers" to the elements of m/m, and this is what the dual space does.