<?xml version="1.0"?>
<div><span class="kw">theorem </span><a NAME="T51"><span class="comment"><font color="firebrick">:: MATRLIN2:51</font></span><br/></a><div class="add"> for <font color="Olive" title="b1">K</font> being   <a href="vectsp_1.html#NM5" title="VECTSP_1:NM.5">Field</a><br/>  for <font color="Olive" title="b2">V1</font>, <font color="Olive" title="b3">V2</font>, <font color="Olive" title="b4">V3</font> being   <a href="matrlin.html#V1" title="MATRLIN:attr.1">finite-dimensional</a>  <a href="vectsp_1.html#NM9" title="VECTSP_1:NM.9">VectSp</a> of <font color="Olive" title="b1">K</font><br/>  for <font color="Olive" title="b5">f</font> being   <a href="ranknull.html#NM1" title="RANKNULL:NM.1">linear-transformation</a> of <font color="Olive" title="b2">V1</font>,<font color="Olive" title="b3">V2</font><br/>  for <font color="Olive" title="b6">g</font> being   <a href="ranknull.html#NM1" title="RANKNULL:NM.1">linear-transformation</a> of <font color="Olive" title="b3">V2</font>,<font color="Olive" title="b4">V3</font>  st <font color="Olive" title="b6">g</font> <a href="matrlin2.html#K8" title="MATRLIN2:func.8">|</a> <span class="p1">(<span class="default"><a href="ranknull.html#K3" title="RANKNULL:func.3">im</a> <font color="Olive" title="b5">f</font></span>)</span> is  <a href="funct_1.html#V2" title="FUNCT_1:attr.2">one-to-one</a>  holds <br/>(  <a href="ranknull.html#K10" title="RANKNULL:func.10">rank</a> <span class="p1">(<span class="default"><font color="Olive" title="b6">g</font> <a href="matrlin2.html#K6" title="MATRLIN2:func.6">*</a> <font color="Olive" title="b5">f</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="ranknull.html#K10" title="RANKNULL:func.10">rank</a> <font color="Olive" title="b5">f</font> &amp;  <a href="ranknull.html#K11" title="RANKNULL:func.11">nullity</a> <span class="p1">(<span class="default"><font color="Olive" title="b6">g</font> <a href="matrlin2.html#K6" title="MATRLIN2:func.6">*</a> <font color="Olive" title="b5">f</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="ranknull.html#K11" title="RANKNULL:func.11">nullity</a> <font color="Olive" title="b5">f</font> )</div></div>
