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:<math>\alpha \mathbf{A} + \beta\mathbf{B} \in M_{mn}(F) </math>
where ''α'' and ''β'' are numbers in ''F''.
Any matrix can be expressed as a linear combination of basis matrices, which play the role of the [[basis vector]]s for the matrix space. For example, for the set of 2×2 matrices over the field of real numbers, ''M''<sub>22</sub>(ℝ), one legitimate basis set of matrices is:
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{{main|Function (mathematics)}}
Matrix elements are not restricted to constant numbers, they can be [[mathematical variable]]s.
===Functions of matrices ===
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[[Category:Matrices]]
[[Category:Numerical analysis]]
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