<?xml version="1.0"?>
<div class="add">

<b>set </b><font color="Maroon" title="c3">vq</font> =  <a href="vectsp10.html#K6" title="VECTSP10:func.6">VectQuot</a> <font color="Maroon" title="c1">V</font>,<span class="p1">(<span class="default"><a href="bilinear.html#K15" title="BILINEAR:func.15">LKer</a> <font color="Maroon" title="c2">f</font></span>)</span>;<br/>
<b>set </b><font color="Maroon" title="c4">vr</font> =  <a href="vectsp10.html#K6" title="VECTSP10:func.6">VectQuot</a> <font color="Maroon" title="c1">V</font>,<span class="p1">(<span class="default"><a href="bilinear.html#K16" title="BILINEAR:func.16">RKer</a> <span class="p2">(<span class="default"><font color="Maroon" title="c2">f</font> <a href="hermitan.html#K3" title="HERMITAN:func.3">*'</a> </span>)</span></span>)</span>;<br/>
<b>set </b><font color="Maroon" title="c5">qh</font> =  <a href="hermitan.html#K9" title="HERMITAN:func.9">ScalarForm</a> <font color="Maroon" title="c2">f</font>;<br/>
<i><font color="Green" title="E62">A1</font></i>:  <a href="bilinear.html#K12" title="BILINEAR:func.12">leftker</a> <span class="p1">(<span class="default"><a href="hermitan.html#K9" title="HERMITAN:func.9">ScalarForm</a> <font color="Maroon" title="c2">f</font></span>)</span> = 
 <a href="bilinear.html#K12" title="BILINEAR:func.12">leftker</a> <span class="p1">(<span class="default"><a href="hermitan.html#K8" title="HERMITAN:func.8">Q*Form</a> <font color="Maroon" title="c2">f</font></span>)</span>
<b>by </b><i><a class="ref" href="hermitan.html#T69" target="_self" title="HERMITAN:th.69">Th69</a></i>
<br/>.= 
<span class="p1"><a href="tarski.html#K1" title="TARSKI:func.1">{</a><span class="default"><span class="p2">(<span class="default"><a href="struct_0.html#K4" title="STRUCT_0:func.4">0.</a> <span class="p3">(<span class="default"><a href="vectsp10.html#K6" title="VECTSP10:func.6">VectQuot</a> <font color="Maroon" title="c1">V</font>,<span class="p4">(<span class="default"><a href="bilinear.html#K15" title="BILINEAR:func.15">LKer</a> <font color="Maroon" title="c2">f</font></span>)</span></span>)</span></span>)</span></span><a href="tarski.html#K1" title="TARSKI:func.1">}</a></span>
<b>by </b><i><a class="ref" href="bilinear.html#D24" title="BILINEAR:def.24">BILINEAR:def 24</a></i>
;<br/>
 <a href="bilinear.html#K13" title="BILINEAR:func.13">rightker</a> <span class="p1">(<span class="default"><a href="hermitan.html#K9" title="HERMITAN:func.9">ScalarForm</a> <font color="Maroon" title="c2">f</font></span>)</span> = 
 <a href="bilinear.html#K13" title="BILINEAR:func.13">rightker</a> <span class="p1">(<span class="default"><a href="hermitan.html#K8" title="HERMITAN:func.8">Q*Form</a> <font color="Maroon" title="c2">f</font></span>)</span>
<b>by </b><i><a class="ref" href="hermitan.html#T59" target="_self" title="HERMITAN:th.59">Th59</a></i>
<br/>.= 
<span class="p1"><a href="tarski.html#K1" title="TARSKI:func.1">{</a><span class="default"><span class="p2">(<span class="default"><a href="struct_0.html#K4" title="STRUCT_0:func.4">0.</a> <span class="p3">(<span class="default"><a href="vectsp10.html#K6" title="VECTSP10:func.6">VectQuot</a> <font color="Maroon" title="c1">V</font>,<span class="p4">(<span class="default"><a href="bilinear.html#K16" title="BILINEAR:func.16">RKer</a> <span class="p5">(<span class="default"><font color="Maroon" title="c2">f</font> <a href="hermitan.html#K3" title="HERMITAN:func.3">*'</a> </span>)</span></span>)</span></span>)</span></span>)</span></span><a href="tarski.html#K1" title="TARSKI:func.1">}</a></span>
<b>by </b><i><a class="ref" href="bilinear.html#D25" title="BILINEAR:def.25">BILINEAR:def 25</a></i>
<br/>.= 
<span class="p1"><a href="tarski.html#K1" title="TARSKI:func.1">{</a><span class="default"><span class="p2">(<span class="default"><a href="struct_0.html#K4" title="STRUCT_0:func.4">0.</a> <span class="p3">(<span class="default"><a href="vectsp10.html#K6" title="VECTSP10:func.6">VectQuot</a> <font color="Maroon" title="c1">V</font>,<span class="p4">(<span class="default"><a href="bilinear.html#K15" title="BILINEAR:func.15">LKer</a> <font color="Maroon" title="c2">f</font></span>)</span></span>)</span></span>)</span></span><a href="tarski.html#K1" title="TARSKI:func.1">}</a></span>
<b>by </b><i><a class="ref" href="hermitan.html#T59" target="_self" title="HERMITAN:th.59">Th59</a></i>
;<br/>
<b>hence </b><a NAME="E3:129_1_1"/><i><font color="Green" title="E63">A2</font></i>: 
( not  <a href="hermitan.html#K9" title="HERMITAN:func.9">ScalarForm</a> <font color="Maroon" title="c2">f</font> is <a href="bilinear.html#V5" title="BILINEAR:attr.5">degenerated-on-left</a> &amp; not  <a href="hermitan.html#K9" title="HERMITAN:func.9">ScalarForm</a> <font color="Maroon" title="c2">f</font> is <a href="bilinear.html#V6" title="BILINEAR:attr.6">degenerated-on-right</a> )
 <b>by </b><i><a class="txt" href="hermitan.html#E1:129_1_1"><i><font color="Green" title="E62">A1</font></i></a>, <a class="ref" href="bilinear.html#D24" title="BILINEAR:def.24">BILINEAR:def 24</a>, <a class="ref" href="bilinear.html#D25" title="BILINEAR:def.25">BILINEAR:def 25</a></i>;<br/>

<b>let </b><font color="Maroon" title="c6">A</font> be   <a href="vectsp_1.html#NM6" title="VECTSP_1:NM.6">Vector</a> of <span class="p1">(<span class="default"><a href="vectsp10.html#K6" title="VECTSP10:func.6">VectQuot</a> <font color="Maroon" title="c1">V</font>,<span class="p2">(<span class="default"><a href="bilinear.html#K15" title="BILINEAR:func.15">LKer</a> <font color="Maroon" title="c2">f</font></span>)</span></span>)</span>; <i><font color="Red">:: according to </font></i><a class="ref" href="hermitan.html#D13" target="_self" title="HERMITAN:def.13">HERMITAN:def 13</a><br/>

<b>assume </b><a NAME="E4:129_1_1"/>
<font color="Maroon" title="c6">A</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a>  <a href="struct_0.html#K4" title="STRUCT_0:func.4">0.</a> <span class="p1">(<span class="default"><a href="vectsp10.html#K6" title="VECTSP10:func.6">VectQuot</a> <font color="Maroon" title="c1">V</font>,<span class="p2">(<span class="default"><a href="bilinear.html#K15" title="BILINEAR:func.15">LKer</a> <font color="Maroon" title="c2">f</font></span>)</span></span>)</span>
 ;<br/>

<a NAME="E5:129_1_1"/><b>then </b>
 <a href="complex1.html#K3" title="COMPLEX1:func.3">Re</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="hermitan.html#K9" title="HERMITAN:func.9">ScalarForm</a> <font color="Maroon" title="c2">f</font></span>)</span> <a href="binop_1.html#K2" title="BINOP_1:func.2">.</a> <font color="Maroon" title="c6">A</font>,<font color="Maroon" title="c6">A</font></span>)</span> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> 0
 
<b>by </b><i><a class="txt" href="hermitan.html#E3:129_1_1"><i><font color="Green" title="E63">A2</font></i></a>, <a class="ref" href="hermitan.html#T61" target="_self" title="HERMITAN:th.61">Th61</a></i>;<br/>
<b>hence </b><a NAME="E6:129_1_1"/>
0 <a href="xxreal_0.html#R1" title="XXREAL_0:pred.1">&lt;</a>  <a href="complex1.html#K3" title="COMPLEX1:func.3">Re</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="hermitan.html#K9" title="HERMITAN:func.9">ScalarForm</a> <font color="Maroon" title="c2">f</font></span>)</span> <a href="binop_1.html#K2" title="BINOP_1:func.2">.</a> <font color="Maroon" title="c6">A</font>,<font color="Maroon" title="c6">A</font></span>)</span>
 <b>by </b><i><a class="ref" href="hermitan.html#D7" target="_self" title="HERMITAN:def.7">Def7</a></i>;<br/>


</div>
