Editing Examples of vector spaces (section)

==Matrices==
Let ''F''<sup>''m''×''n''</sup> denote the set of ''m''×''n'' [[Matrix (mathematics)|matrices]] with entries in ''F''. Then ''F''<sup>''m''×''n''</sup> is a vector space over ''F''. Vector addition is just matrix addition and scalar multiplication is defined in the obvious way (by multiplying each entry by the same scalar). The zero vector is just the [[zero matrix]]. The [[dimension (vector space)|dimension]] of ''F''<sup>''m''×''n''</sup> is ''mn''. One possible choice of basis is the matrices with a single entry equal to 1 and all other entries 0.

When ''m'' = ''n'' the matrix is [[Square matrix|square]] and [[matrix multiplication]] of two such matrices produces a third. This vector space of dimension ''n''<sup>2</sup> forms an [[algebra over a field]].