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<div><span class="kw">theorem </span><a NAME="T25"><span class="comment"><font color="firebrick">:: ZMODUL05:25</font></span><br/></a><div class="add"> for <font color="Olive" title="b1">V</font>, <font color="Olive" title="b2">W</font> being   <a href="zmodul01.html#NM1" title="ZMODUL01:NM.1">Z_Module</a><br/>  for <font color="Olive" title="b3">T</font> being   <a href="ranknull.html#NM1" title="RANKNULL:NM.1">linear-transformation</a> of <font color="Olive" title="b1">V</font>,<font color="Olive" title="b2">W</font>  st <font color="Olive" title="b3">T</font> is  <a href="funct_1.html#V2" title="FUNCT_1:attr.2">one-to-one</a>  holds <br/> <a href="ranknull.html#K1" title="RANKNULL:func.1">ker</a> <font color="Olive" title="b3">T</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="vectsp_4.html#K1" title="VECTSP_4:func.1">(0).</a> <font color="Olive" title="b1">V</font> <span class="kw">by</span> <span class="lab"><a class="ref" href="ranknull.html#T15" onmouseover="rs('ranknull/T15')" onmouseout="rh()">RANKNULL:15</a></span>;<br/></div></div>
