<?xml version="1.0"?>
<div><span class="kw">theorem </span><span class="lab"><font color="Green" title="E28">Th28</font></span>: <a NAME="T27"><span class="comment"><font color="firebrick">:: REAL_NS3:27</font></span><br/></a><div class="add"> for <font color="Olive" title="b1">V</font> being   <a href="rlvect_5.html#V1" title="RLVECT_5:attr.1">finite-dimensional</a>  <a href="normsp_1.html#NM1" title="NORMSP_1:NM.1">RealNormSpace</a>  st  <a href="rlvect_5.html#K1" title="RLVECT_5:func.1">dim</a> <font color="Olive" title="b1">V</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a>  <a href="numbers.html#K5" title="NUMBERS:func.5">0</a>  holds <br/> ex <font color="Olive" title="b2">L</font> being   <a href="lopban_1.html#NM1" title="LOPBAN_1:NM.1">LinearOperator</a> of <font color="Olive" title="b1">V</font>,<span class="p1">(<span class="default"><a href="real_ns1.html#K4" title="REAL_NS1:func.4">REAL-NS</a> <span class="p2">(<span class="default"><a href="rlvect_5.html#K1" title="RLVECT_5:func.1">dim</a> <font color="Olive" title="b1">V</font></span>)</span></span>)</span> st <br/>( <font color="Olive" title="b2">L</font> is  <a href="funct_1.html#V2" title="FUNCT_1:attr.2">one-to-one</a>  &amp; <font color="Olive" title="b2">L</font> is  <a href="funct_2.html#V2" title="FUNCT_2:attr.2">onto</a>  &amp; <font color="Olive" title="b2">L</font> is  <a href="real_ns3.html#V1" title="REAL_NS3:attr.1">isometric-like</a>  )</div></div>
