The set of all ''m''×''n'' matrices over a number [[field (mathematics)|field]] ''F'' denoted in this article ''M''<sub>''mn''</sub>(''F'') form a [[vector space]]. Examples of ''F'' include the set of [[integerrational number]]s ℤℚ, the [[real number]]s ℝ, and set of [[complex number]]s ℂ. The spaces ''M''<sub>''mn''</sub>(''F'') and ''M''<sub>''pq''</sub>(''F'') are different spaces if ''m'' and ''p'' are unequal, and if ''n'' and ''q'' are unequal; for instance ''M''<sub>32</sub>(''F'') ≠ ''M''<sub>23</sub>(''F''). Two ''m''×''n'' matrices '''A''' and '''B''' in ''M''<sub>''mn''</sub>(''F'') can be added together to form another matrix in the space ''M''<sub>''mn''</sub>(''F''):
