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<b>set </b><font color="Maroon">vq</font> =  <a href="vectsp10.html#K6">VectQuot</a> <font color="Maroon">V</font>,<span class="p1">(<span class="default"><a href="bilinear.html#K15">LKer</a> <font color="Maroon">f</font></span>)</span>;<br/>
<b>set </b><font color="Maroon">vr</font> =  <a href="vectsp10.html#K6">VectQuot</a> <font color="Maroon">V</font>,<span class="p1">(<span class="default"><a href="bilinear.html#K16">RKer</a> <span class="p2">(<span class="default"><font color="Maroon">f</font> <a href="hermitan.html#K3" target="_self">*'</a> </span>)</span></span>)</span>;<br/>
<b>set </b><font color="Maroon">qh</font> =  <a href="hermitan.html#K9" target="_self">ScalarForm</a> <font color="Maroon">f</font>;<br/>
<i><font color="Green">E30</font></i>:  <a href="bilinear.html#K12">leftker</a> <span class="p1">(<span class="default"><a href="hermitan.html#K9" target="_self">ScalarForm</a> <font color="Maroon">f</font></span>)</span> = 
 <a href="bilinear.html#K12">leftker</a> <span class="p1">(<span class="default"><a href="hermitan.html#K8" target="_self">Q*Form</a> <font color="Maroon">f</font></span>)</span>
<b>by </b><i><a class="ref" href="hermitan.html#T21" target="_self">Th21</a></i>
<br/>.= 
<span class="p1"><a href="tarski.html#K1">{</a><span class="default"><span class="p2">(<span class="default"><a href="rlvect_1.html#K1">0.</a> <span class="p3">(<span class="default"><a href="vectsp10.html#K6">VectQuot</a> <font color="Maroon">V</font>,<span class="p4">(<span class="default"><a href="bilinear.html#K15">LKer</a> <font color="Maroon">f</font></span>)</span></span>)</span></span>)</span></span><a href="tarski.html#K1">}</a></span>
<b>by </b><i><a class="ref" href="bilinear.html#D24">BILINEAR:def 24</a></i>
;<br/>
 <a href="bilinear.html#K13">rightker</a> <span class="p1">(<span class="default"><a href="hermitan.html#K9" target="_self">ScalarForm</a> <font color="Maroon">f</font></span>)</span> = 
 <a href="bilinear.html#K13">rightker</a> <span class="p1">(<span class="default"><a href="hermitan.html#K8" target="_self">Q*Form</a> <font color="Maroon">f</font></span>)</span>
<b>by </b><i><a class="ref" href="hermitan.html#T22" target="_self">Th22</a></i>
<br/>.= 
<span class="p1"><a href="tarski.html#K1">{</a><span class="default"><span class="p2">(<span class="default"><a href="rlvect_1.html#K1">0.</a> <span class="p3">(<span class="default"><a href="vectsp10.html#K6">VectQuot</a> <font color="Maroon">V</font>,<span class="p4">(<span class="default"><a href="bilinear.html#K16">RKer</a> <span class="p5">(<span class="default"><font color="Maroon">f</font> <a href="hermitan.html#K3" target="_self">*'</a> </span>)</span></span>)</span></span>)</span></span>)</span></span><a href="tarski.html#K1">}</a></span>
<b>by </b><i><a class="ref" href="bilinear.html#D25">BILINEAR:def 25</a></i>
<br/>.= 
<span class="p1"><a href="tarski.html#K1">{</a><span class="default"><span class="p2">(<span class="default"><a href="rlvect_1.html#K1">0.</a> <span class="p3">(<span class="default"><a href="vectsp10.html#K6">VectQuot</a> <font color="Maroon">V</font>,<span class="p4">(<span class="default"><a href="bilinear.html#K15">LKer</a> <font color="Maroon">f</font></span>)</span></span>)</span></span>)</span></span><a href="tarski.html#K1">}</a></span>
<b>by </b><i><a class="ref" href="hermitan.html#T18" target="_self">Th18</a></i>
;<br/>
<b>hence </b><a NAME="E3:129_1_1"/><i><font color="Green">E31</font></i>: 
( not  <a href="hermitan.html#K9" target="_self">ScalarForm</a> <font color="Maroon">f</font> is <a href="bilinear.html#V5">degenerated-on-left</a> &amp; not  <a href="hermitan.html#K9" target="_self">ScalarForm</a> <font color="Maroon">f</font> is <a href="bilinear.html#V6">degenerated-on-right</a> )
 <b>by </b><i><a class="ref" href="hermitan.html#T25" target="_self">Th25</a>, <a class="ref" href="bilinear.html#D24">BILINEAR:def 24</a>, <a class="ref" href="bilinear.html#D25">BILINEAR:def 25</a></i>;<br/>

<b>let </b><font color="Maroon">A</font> be   <a href="vectsp_1.html#NM5">Vector</a> of <span class="p1">(<span class="default"><a href="vectsp10.html#K6">VectQuot</a> <font color="Maroon">V</font>,<span class="p2">(<span class="default"><a href="bilinear.html#K15">LKer</a> <font color="Maroon">f</font></span>)</span></span>)</span>; <i><font color="Red">:: according to </font></i><a class="ref" href="hermitan.html#D13" target="_self">HERMITAN:def 13</a><br/>

<b>assume </b><a NAME="E4:129_1_1"/>
<font color="Maroon">A</font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a>  <a href="rlvect_1.html#K1">0.</a> <span class="p1">(<span class="default"><a href="vectsp10.html#K6">VectQuot</a> <font color="Maroon">V</font>,<span class="p2">(<span class="default"><a href="bilinear.html#K15">LKer</a> <font color="Maroon">f</font></span>)</span></span>)</span>
 ;<br/>

<a NAME="E5:129_1_1"/><b>then </b>
 <a href="complex1.html#K3">Re</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="hermitan.html#K9" target="_self">ScalarForm</a> <font color="Maroon">f</font></span>)</span> <a href="binop_1.html#K2">.</a> <font color="Maroon">A</font>,<font color="Maroon">A</font></span>)</span> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a> 0
 
<b>by </b><i><a class="ref" href="hermitan.html#T26" target="_self">Th26</a>, </i>;<br/>
<b>hence </b><a NAME="E6:129_1_1"/>
0 <a href="xxreal_0.html#R1">&lt;</a>  <a href="complex1.html#K3">Re</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="hermitan.html#K9" target="_self">ScalarForm</a> <font color="Maroon">f</font></span>)</span> <a href="binop_1.html#K2">.</a> <font color="Maroon">A</font>,<font color="Maroon">A</font></span>)</span>
 <b>by </b><i><a class="txt" href="hermitan.html#E3:129_1_1"><i><font color="Green">E31</font></i></a></i>;<br/>


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