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<b>let </b><font color="Maroon" title="c1">V</font> be   <a href="vectsp_1.html#NM7" title="VECTSP_1:NM.7">VectSp</a> of  <a href="complfld.html#K1" title="COMPLFLD:func.1">F_Complex</a> ;<br/><b>let </b><font color="Maroon" title="c2">f</font> be  <a href="hermitan.html#V5" title="HERMITAN:attr.5">diagReR+0valued</a> <a href="hermitan.html#NM3" title="HERMITAN:NM.3">hermitan-Form</a> of <font color="Maroon" title="c1">V</font>;<br/><b>let </b><font color="Maroon" title="c3">v</font> be   <a href="vectsp_1.html#NM6" title="VECTSP_1:NM.6">Vector</a> of <font color="Maroon" title="c1">V</font>;<br/>





<b>assume </b><b>that </b><br/><a NAME="E1:109"/><i><font color="Green" title="E53">A1</font></i>: 
 <a href="complex1.html#K3" title="COMPLEX1:func.3">Re</a> <span class="p1">(<span class="default"><font color="Maroon" title="c2">f</font> <a href="binop_1.html#K2" title="BINOP_1:func.2">.</a> <font color="Maroon" title="c3">v</font>,<font color="Maroon" title="c3">v</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> 0
 <b>and </b><br/><a NAME="E2:109"/><i><font color="Green" title="E54">A2</font></i>: 
(  not <font color="Maroon" title="c2">f</font> is <a href="bilinear.html#V5" title="BILINEAR:attr.5">degenerated-on-left</a> or  not <font color="Maroon" title="c2">f</font> is <a href="bilinear.html#V6" title="BILINEAR:attr.6">degenerated-on-right</a> )
 ;<br/>

<a NAME="E3:109"/>
<font color="Maroon" title="c2">f</font> <a href="binop_1.html#K2" title="BINOP_1:func.2">.</a> <font color="Maroon" title="c3">v</font>,<font color="Maroon" title="c3">v</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="struct_0.html#K4" title="STRUCT_0:func.4">0.</a> <a href="complfld.html#K1" title="COMPLFLD:func.1">F_Complex</a> 
 
<b>by </b><i><a class="txt" href="hermitan.html#E1:109"><i><font color="Green" title="E53">A1</font></i></a>, <a class="ref" href="hermitan.html#T60" target="_self" title="HERMITAN:th.60">Th60</a></i>;<br/>
<a NAME="E4:109"/><b>then </b><i><font color="Green" title="E55">A3</font></i>: 
<font color="Maroon" title="c3">v</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <span class="p1">{<span class="default"> <font color="Olive" title="b1">w</font> where <font color="Olive" title="b1">w</font> is   <a href="vectsp_1.html#NM6" title="VECTSP_1:NM.6">Vector</a> of <font color="Maroon" title="c1">V</font> : <font color="Maroon" title="c2">f</font> <a href="binop_1.html#K2" title="BINOP_1:func.2">.</a> <font color="Olive" title="b1">w</font>,<font color="Olive" title="b1">w</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="struct_0.html#K4" title="STRUCT_0:func.4">0.</a> <a href="complfld.html#K1" title="COMPLFLD:func.1">F_Complex</a>  </span>}</span> 
 
;<br/>
<div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="109_1"><b>per </b></a><a class="txt" onclick="hs(this)" href="javascript:()"><b>cases </b></a><span class="hide"><a NAME="E1:109_1"/>
(  not <font color="Maroon" title="c2">f</font> is <a href="bilinear.html#V5" title="BILINEAR:attr.5">degenerated-on-left</a> or  not <font color="Maroon" title="c2">f</font> is <a href="bilinear.html#V6" title="BILINEAR:attr.6">degenerated-on-right</a> )
 </span><b>by </b><i><a class="txt" href="hermitan.html#E2:109"><i><font color="Green" title="E54">A2</font></i></a></i>;<br/><div class="add"><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="109_1_1"><b>suppose </b></a><a NAME="E1:109_1_1"/>
not <font color="Maroon" title="c2">f</font> is <a href="bilinear.html#V5" title="BILINEAR:attr.5">degenerated-on-left</a>
 ;<br/><div class="add"><b>then </b><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> <font color="Maroon" title="c1">V</font></span>)</span></span><a href="tarski.html#K1" title="TARSKI:func.1">}</a></span> = 
 <a href="bilinear.html#K12" title="BILINEAR:func.12">leftker</a> <font color="Maroon" title="c2">f</font>
<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#K14" title="BILINEAR:func.14">diagker</a> <font color="Maroon" title="c2">f</font>
<b>by </b><i><a class="ref" href="hermitan.html#T55" target="_self" title="HERMITAN:th.55">Th55</a></i>
;<br/><b>hence </b><a NAME="E3:109_1_1"/>
<font color="Maroon" title="c3">v</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="struct_0.html#K4" title="STRUCT_0:func.4">0.</a> <font color="Maroon" title="c1">V</font>
 <b>by </b><i><a class="txt" href="hermitan.html#E4:109"><i><font color="Green" title="E55">A3</font></i></a>, <a class="ref" href="tarski.html#D1" title="TARSKI:def.1">TARSKI:def 1</a></i>;<br/></div><b>end;</b></div><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="109_1_2"><b>suppose </b></a><a NAME="E1:109_1_2"/>
not <font color="Maroon" title="c2">f</font> is <a href="bilinear.html#V6" title="BILINEAR:attr.6">degenerated-on-right</a>
 ;<br/><div class="add"><b>then </b><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> <font color="Maroon" title="c1">V</font></span>)</span></span><a href="tarski.html#K1" title="TARSKI:func.1">}</a></span> = 
 <a href="bilinear.html#K13" title="BILINEAR:func.13">rightker</a> <font color="Maroon" title="c2">f</font>
<b>by </b><i><a class="ref" href="bilinear.html#D25" title="BILINEAR:def.25">BILINEAR:def 25</a></i>
<br/>.= 
 <a href="bilinear.html#K14" title="BILINEAR:func.14">diagker</a> <font color="Maroon" title="c2">f</font>
<b>by </b><i><a class="ref" href="hermitan.html#T56" target="_self" title="HERMITAN:th.56">Th56</a></i>
;<br/><b>hence </b><a NAME="E3:109_1_2"/>
<font color="Maroon" title="c3">v</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="struct_0.html#K4" title="STRUCT_0:func.4">0.</a> <font color="Maroon" title="c1">V</font>
 <b>by </b><i><a class="txt" href="hermitan.html#E4:109"><i><font color="Green" title="E55">A3</font></i></a>, <a class="ref" href="tarski.html#D1" title="TARSKI:def.1">TARSKI:def 1</a></i>;<br/></div><b>end;</b></div></div><b>end;</b></div>

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