Here is the vector space of linear maps from to .

Let be given by and a linear map.

We can define a continuous random field well enough as a linear map from a space of functions into the real numbers.

A single linear map may be represented by many matrices.

No classification of linear maps could hope to be exhaustive.

Discontinuous linear maps can be proven to exist more generally even if the space is complete.

There is a simple way to make precise sense of differentials by regarding them as linear maps.

Both examples have the property that any continuous linear map to the real numbers is 0.

If X is infinite-dimensional, there exist linear maps which are not continuous.

An important special case is the kernel of a linear map.