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Now let φ be any [[functional]] of V, that is, φ is a function (mapping) from V to '''F''' so that for any ''t'' in '''F''' and ''u'',''v'' in V:
:<math>
\phi\left(tu+v\right)=t\phi\left(u\right)+\phi\left(v\right)
</math>
(''[[linear]]'' [[functional]]).
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