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<p> (the converse is also true).</p>

<p>For example, if  and  then the assignment  and  can be linearly extended from the linearly independent set of vectors  to a linear map on . The unique linear extension  is the map that sends  to</p>

<p>Every (scalar-valued) <a href="page.php?w=linear_functional">linear functional</a>  defined on a <a href="page.php?w=vector_subspace">vector subspace</a> of a real or complex vector space  has a linear extension to all of .Indeed, the <a href="page.php?w=Hahn-Banach_theorem">Hahn-Banach dominated extension theorem</a></p><p>
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