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

<b>let </b><font color="Maroon">c<sub>1</sub></font> be   <a href="vectsp_1.html#NM6">VectSp</a> of  <a href="complfld.html#K1">F_Complex</a> ;<br/><b>let </b><font color="Maroon">c<sub>2</sub></font> be  <a href="hermitan.html#V5" target="_self">diagReR+0valued</a> <a href="hermitan.html#NM3">hermitan-Form</a> of <font color="Maroon">c<sub>1</sub></font>;<br/><b>let </b><font color="Maroon">c<sub>3</sub></font> be   <a href="vectsp_1.html#NM5">Vector</a> of <font color="Maroon">c<sub>1</sub></font>;<br/>





<b>assume </b><b>that </b><br/><a NAME="E1:111"/><i><font color="Green">E58</font></i>: 
 <a href="complex1.html#K3">Re</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>2</sub></font> <a href="binop_1.html#K2">.</a> <font color="Maroon">c<sub>3</sub></font>,<font color="Maroon">c<sub>3</sub></font></span>)</span> <a href="hidden.html#R1">=</a> 0
 <b>and </b><br/><a NAME="E2:111"/><i><font color="Green">E59</font></i>: 
(  not <font color="Maroon">c<sub>2</sub></font> is <a href="bilinear.html#V5">degenerated-on-left</a> or  not <font color="Maroon">c<sub>2</sub></font> is <a href="bilinear.html#V6">degenerated-on-right</a> )
 ;<br/>

<a NAME="E3:111"/>
<font color="Maroon">c<sub>2</sub></font> <a href="binop_1.html#K2">.</a> <font color="Maroon">c<sub>3</sub></font>,<font color="Maroon">c<sub>3</sub></font> <a href="hidden.html#R1">=</a>  <a href="rlvect_1.html#K1">0.</a> <a href="complfld.html#K1">F_Complex</a> 
 
<b>by </b><i><a class="txt" href="hermitan.html#E1:111"><i><font color="Green">E58</font></i></a>, <a class="ref" href="hermitan.html#T60" target="_self">Th60</a></i>;<br/>
<a NAME="E4:111"/><b>then </b>
<font color="Maroon">c<sub>3</sub></font> <a href="hidden.html#R2">in</a> <span class="p1">{<span class="default"> <font color="Olive">b<sub>1</sub></font> where B is   <a href="vectsp_1.html#NM5">Vector</a> of <font color="Maroon">c<sub>1</sub></font> : <font color="Maroon">c<sub>2</sub></font> <a href="binop_1.html#K2">.</a> <font color="Olive">b<sub>1</sub></font>,<font color="Olive">b<sub>1</sub></font> <a href="hidden.html#R1">=</a>  <a href="rlvect_1.html#K1">0.</a> <a href="complfld.html#K1">F_Complex</a>  </span>}</span> 
 
;<br/>
<a NAME="E5:111"/><b>then </b><i><font color="Green">E60</font></i>: 
<font color="Maroon">c<sub>3</sub></font> <a href="hidden.html#R2">in</a>  <a href="bilinear.html#K14">diagker</a> <font color="Maroon">c<sub>2</sub></font>
 
;<br/>
<div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="111_1"><b>per </b></a><a class="txt" onclick="hs(this)" href="javascript:()"><b>cases </b></a><span class="hide"><a NAME="E1:111_1"/>
(  not <font color="Maroon">c<sub>2</sub></font> is <a href="bilinear.html#V5">degenerated-on-left</a> or  not <font color="Maroon">c<sub>2</sub></font> is <a href="bilinear.html#V6">degenerated-on-right</a> )
 </span><b>by </b><i><a class="txt" href="hermitan.html#E2:111"><i><font color="Green">E59</font></i></a></i>;<br/><div class="add"><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="111_1_1"><b>suppose </b></a><a NAME="E1:111_1_1"/>
not <font color="Maroon">c<sub>2</sub></font> is <a href="bilinear.html#V5">degenerated-on-left</a>
 ;<br/><div class="add"><b>then </b><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> <font color="Maroon">c<sub>1</sub></font></span>)</span></span><a href="tarski.html#K1">}</a></span> = 
 <a href="bilinear.html#K12">leftker</a> <font color="Maroon">c<sub>2</sub></font>
<b>by </b><i><a class="ref" href="bilinear.html#D24">BILINEAR:def 24</a></i>
<br/>.= 
 <a href="bilinear.html#K14">diagker</a> <font color="Maroon">c<sub>2</sub></font>
<b>by </b><i><a class="ref" href="hermitan.html#T55" target="_self">Th55</a></i>
;<br/><b>hence </b><a NAME="E3:111_1_1"/>
<font color="Maroon">c<sub>3</sub></font> <a href="hidden.html#R1">=</a>  <a href="rlvect_1.html#K1">0.</a> <font color="Maroon">c<sub>1</sub></font>
 <b>by </b><i><a class="txt" href="hermitan.html#E5:111"><i><font color="Green">E60</font></i></a>, <a class="ref" href="tarski.html#D1">TARSKI:def 1</a></i>;<br/></div><b>end;</b></div><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="111_1_2"><b>suppose </b></a><a NAME="E1:111_1_2"/>
not <font color="Maroon">c<sub>2</sub></font> is <a href="bilinear.html#V6">degenerated-on-right</a>
 ;<br/><div class="add"><b>then </b><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> <font color="Maroon">c<sub>1</sub></font></span>)</span></span><a href="tarski.html#K1">}</a></span> = 
 <a href="bilinear.html#K13">rightker</a> <font color="Maroon">c<sub>2</sub></font>
<b>by </b><i><a class="ref" href="bilinear.html#D25">BILINEAR:def 25</a></i>
<br/>.= 
 <a href="bilinear.html#K14">diagker</a> <font color="Maroon">c<sub>2</sub></font>
<b>by </b><i><a class="ref" href="hermitan.html#T56" target="_self">Th56</a></i>
;<br/><b>hence </b><a NAME="E3:111_1_2"/>
<font color="Maroon">c<sub>3</sub></font> <a href="hidden.html#R1">=</a>  <a href="rlvect_1.html#K1">0.</a> <font color="Maroon">c<sub>1</sub></font>
 <b>by </b><i><a class="txt" href="hermitan.html#E5:111"><i><font color="Green">E60</font></i></a>, <a class="ref" href="tarski.html#D1">TARSKI:def 1</a></i>;<br/></div><b>end;</b></div></div><b>end;</b></div>

</div>
