Editing Examples of vector spaces (section)

===Linear maps===
An important example arising in the context of [[linear algebra]] itself is the vector space of [[linear map]]s. Let ''L''(''V'',''W'') denote the set of all linear maps from ''V'' to ''W'' (both of which are vector spaces over ''F''). Then ''L''(''V'',''W'') is a subspace of ''W''<sup>''V''</sup> since it is closed under addition and scalar multiplication.

Note that L(''F''<sup>''n''</sup>,''F''<sup>''m''</sup>) can be identified with the space of matrices ''F''<sup>''m''×''n''</sup> in a natural way.  In fact, by choosing appropriate bases for finite-dimensional spaces V and W, L(V,W) can also be identified with ''F''<sup>''m''×''n''</sup>.  This identification normally depends on the choice of basis.