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

<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/>
<a NAME="E1:126_1_1"/>
 <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> <a href="hidden.html#R1">=</a>  <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>
 
<b>by </b><i><a class="ref" href="hermitan.html#T18" target="_self">Th18</a></i>;<br/>
<b>then reconsider </b><font color="Maroon">sc</font> =  <a href="hermitan.html#K8" target="_self">Q*Form</a> <font color="Maroon">f</font> as   <a href="bilinear.html#NM1">Form</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>,<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="E3:126_1_1"/><i><font color="Green">E30</font></i>: 
<font color="Maroon">sc</font> is <a href="bilinear.html#V4">homogeneousSAF</a>
 
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="126_1_1_1"><b>proof </b></a><div class="add">

<b>let </b><font color="Maroon">w</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="bilinear.html#D15">BILINEAR:def 15</a><br/>

<b>reconsider </b><font color="Maroon">A</font> = <font color="Maroon">w</font> as   <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#K16">RKer</a> <span class="p3">(<span class="default"><font color="Maroon">f</font> <a href="hermitan.html#K3" target="_self">*'</a> </span>)</span></span>)</span></span>)</span> <b>by </b><i><a class="ref" href="hermitan.html#T18" target="_self">Th18</a></i>;<br/>
<b>consider </b><font color="Maroon">wa</font> being   <a href="vectsp_1.html#NM5">Vector</a> of <font color="Maroon">V</font><b> such that </b><br/><a NAME="E3:126_1_1_1"/><i><font color="Green">E31</font></i>: 
<font color="Maroon">A</font> <a href="hidden.html#R1">=</a> <font color="Maroon">wa</font> <a href="vectsp_4.html#K3">+</a> <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>
 <b>by </b><i><a class="ref" href="vectsp10.html#T23">VECTSP10:23</a></i>;<br/>
<b>set </b><font color="Maroon">fg</font> =  <a href="bilinear.html#K10">FunctionalSAF</a> <font color="Maroon">sc</font>,<font color="Maroon">w</font>;<br/>
<b>let </b><font color="Maroon">v</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="hahnban1.html#D12">HAHNBAN1:def 12</a><br/><b>let </b><font color="Maroon">r</font> be   <a href="vectsp_1.html#NM4">Scalar</a> of ;<br/>



<b>consider </b><font color="Maroon">va</font> being   <a href="vectsp_1.html#NM5">Vector</a> of <font color="Maroon">V</font><b> such that </b><br/><a NAME="E5:126_1_1_1"/><i><font color="Green">E32</font></i>: 
<font color="Maroon">v</font> <a href="hidden.html#R1">=</a> <font color="Maroon">va</font> <a href="vectsp_4.html#K3">+</a> <span class="p1">(<span class="default"><a href="bilinear.html#K15">LKer</a> <font color="Maroon">f</font></span>)</span>
 <b>by </b><i><a class="ref" href="vectsp10.html#T23">VECTSP10:23</a></i>;<br/>
<a NAME="E6:126_1_1_1"/><i><font color="Green">E33</font></i>: 
<font color="Maroon">r</font> <a href="vectsp_1.html#K6">*</a> <font color="Maroon">v</font> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><font color="Maroon">r</font> <a href="vectsp_1.html#K6">*</a> <font color="Maroon">va</font></span>)</span> <a href="vectsp_4.html#K3">+</a> <span class="p1">(<span class="default"><a href="bilinear.html#K15">LKer</a> <font color="Maroon">f</font></span>)</span>
 
<b>by </b><i><a class="ref" href="hermitan.html#T25" target="_self">Th25</a>, <a class="ref" href="vectsp10.html#T26">VECTSP10:26</a></i>;<br/>
<b>thus </b><span class="p1">(<span class="default"><a href="bilinear.html#K10">FunctionalSAF</a> <font color="Maroon">sc</font>,<font color="Maroon">w</font></span>)</span> <a href="funct_2.html#K3">.</a> <span class="p1">(<span class="default"><font color="Maroon">r</font> <a href="vectsp_1.html#K6">*</a> <font color="Maroon">v</font></span>)</span> = 
<span class="p1">(<span class="default"><a href="hermitan.html#K8" target="_self">Q*Form</a> <font color="Maroon">f</font></span>)</span> <a href="binop_1.html#K1">.</a> <span class="p1">(<span class="default"><font color="Maroon">r</font> <a href="vectsp_1.html#K6">*</a> <font color="Maroon">v</font></span>)</span>,<font color="Maroon">w</font>
<b>by </b><i><a class="ref" href="bilinear.html#T10">BILINEAR:10</a></i>
<br/>.= 
<font color="Maroon">f</font> <a href="binop_1.html#K2">.</a> <span class="p1">(<span class="default"><font color="Maroon">r</font> <a href="vectsp_1.html#K6">*</a> <font color="Maroon">va</font></span>)</span>,<font color="Maroon">wa</font>
<b>by </b><i><a class="ref" href="hermitan.html#T22" target="_self">Th22</a>, <a class="ref" href="hermitan.html#T26" target="_self">Th26</a>, </i>
<br/>.= 
<font color="Maroon">r</font> <a href="group_1.html#K10">*</a> <span class="p1">(<span class="default"><font color="Maroon">f</font> <a href="binop_1.html#K2">.</a> <font color="Maroon">va</font>,<font color="Maroon">wa</font></span>)</span>
<b>by </b><i><a class="ref" href="bilinear.html#T32">BILINEAR:32</a></i>
<br/>.= 
<font color="Maroon">r</font> <a href="group_1.html#K10">*</a> <span class="p1">(<span class="default"><font color="Maroon">sc</font> <a href="binop_1.html#K2">.</a> <font color="Maroon">v</font>,<font color="Maroon">w</font></span>)</span>
<b>by </b><i><a class="ref" href="hermitan.html#T22" target="_self">Th22</a>, <a class="ref" href="hermitan.html#T25" target="_self">Th25</a>, </i>
<br/>.= 
<font color="Maroon">r</font> <a href="group_1.html#K10">*</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="bilinear.html#K10">FunctionalSAF</a> <font color="Maroon">sc</font>,<font color="Maroon">w</font></span>)</span> <a href="funct_2.html#K3">.</a> <font color="Maroon">v</font></span>)</span>
<b>by </b><i><a class="ref" href="bilinear.html#T10">BILINEAR:10</a></i>
;<br/>


</div><b>end;</b></div>
<a NAME="E4:126_1_1"/><i><font color="Green">E34</font></i>: 
<font color="Maroon">sc</font> is <a href="bilinear.html#V2">additiveSAF</a>
 
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="126_1_1_2"><b>proof </b></a><div class="add">

<b>let </b><font color="Maroon">w</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="bilinear.html#D13">BILINEAR:def 13</a><br/>

<b>reconsider </b><font color="Maroon">A</font> = <font color="Maroon">w</font> as   <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#K16">RKer</a> <span class="p3">(<span class="default"><font color="Maroon">f</font> <a href="hermitan.html#K3" target="_self">*'</a> </span>)</span></span>)</span></span>)</span> <b>by </b><i><a class="ref" href="hermitan.html#T18" target="_self">Th18</a></i>;<br/>
<b>consider </b><font color="Maroon">wa</font> being   <a href="vectsp_1.html#NM5">Vector</a> of <font color="Maroon">V</font><b> such that </b><br/><a NAME="E3:126_1_1_2"/><i><font color="Green">E81</font></i>: 
<font color="Maroon">A</font> <a href="hidden.html#R1">=</a> <font color="Maroon">wa</font> <a href="vectsp_4.html#K3">+</a> <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>
 <b>by </b><i><a class="ref" href="vectsp10.html#T23">VECTSP10:23</a></i>;<br/>
<b>set </b><font color="Maroon">fg</font> =  <a href="bilinear.html#K10">FunctionalSAF</a> <font color="Maroon">sc</font>,<font color="Maroon">w</font>;<br/>
<b>let </b><font color="Maroon">v1</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>, <font color="Maroon">v2</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="hahnban1.html#D11">HAHNBAN1:def 11</a><br/>

<b>consider </b><font color="Maroon">va</font> being   <a href="vectsp_1.html#NM5">Vector</a> of <font color="Maroon">V</font><b> such that </b><br/><a NAME="E5:126_1_1_2"/><i><font color="Green">E129</font></i>: 
<font color="Maroon">v1</font> <a href="hidden.html#R1">=</a> <font color="Maroon">va</font> <a href="vectsp_4.html#K3">+</a> <span class="p1">(<span class="default"><a href="bilinear.html#K15">LKer</a> <font color="Maroon">f</font></span>)</span>
 <b>by </b><i><a class="ref" href="vectsp10.html#T23">VECTSP10:23</a></i>;<br/>
<b>consider </b><font color="Maroon">vb</font> being   <a href="vectsp_1.html#NM5">Vector</a> of <font color="Maroon">V</font><b> such that </b><br/><a NAME="E7:126_1_1_2"/><i><font color="Green">E130</font></i>: 
<font color="Maroon">v2</font> <a href="hidden.html#R1">=</a> <font color="Maroon">vb</font> <a href="vectsp_4.html#K3">+</a> <span class="p1">(<span class="default"><a href="bilinear.html#K15">LKer</a> <font color="Maroon">f</font></span>)</span>
 <b>by </b><i><a class="ref" href="vectsp10.html#T23">VECTSP10:23</a></i>;<br/>
<a NAME="E8:126_1_1_2"/><i><font color="Green">E131</font></i>: 
<font color="Maroon">v1</font> <a href="rlvect_1.html#K4">+</a> <font color="Maroon">v2</font> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><font color="Maroon">va</font> <a href="rlvect_1.html#K4">+</a> <font color="Maroon">vb</font></span>)</span> <a href="vectsp_4.html#K3">+</a> <span class="p1">(<span class="default"><a href="bilinear.html#K15">LKer</a> <font color="Maroon">f</font></span>)</span>
 
<b>by </b><i><a class="ref" href="hermitan.html#T26" target="_self">Th26</a>, <a class="ref" href="hermitan.html#T28" target="_self">Th28</a>, <a class="ref" href="vectsp10.html#T27">VECTSP10:27</a></i>;<br/>
<b>thus </b><span class="p1">(<span class="default"><a href="bilinear.html#K10">FunctionalSAF</a> <font color="Maroon">sc</font>,<font color="Maroon">w</font></span>)</span> <a href="funct_2.html#K3">.</a> <span class="p1">(<span class="default"><font color="Maroon">v1</font> <a href="rlvect_1.html#K4">+</a> <font color="Maroon">v2</font></span>)</span> = 
<span class="p1">(<span class="default"><a href="hermitan.html#K8" target="_self">Q*Form</a> <font color="Maroon">f</font></span>)</span> <a href="binop_1.html#K1">.</a> <span class="p1">(<span class="default"><font color="Maroon">v1</font> <a href="rlvect_1.html#K4">+</a> <font color="Maroon">v2</font></span>)</span>,<font color="Maroon">w</font>
<b>by </b><i><a class="ref" href="bilinear.html#T10">BILINEAR:10</a></i>
<br/>.= 
<font color="Maroon">f</font> <a href="binop_1.html#K2">.</a> <span class="p1">(<span class="default"><font color="Maroon">va</font> <a href="rlvect_1.html#K4">+</a> <font color="Maroon">vb</font></span>)</span>,<font color="Maroon">wa</font>
<b>by </b><i><a class="ref" href="hermitan.html#T25" target="_self">Th25</a>, , </i>
<br/>.= 
<span class="p1">(<span class="default"><font color="Maroon">f</font> <a href="binop_1.html#K2">.</a> <font color="Maroon">va</font>,<font color="Maroon">wa</font></span>)</span> <a href="rlvect_1.html#K4">+</a> <span class="p1">(<span class="default"><font color="Maroon">f</font> <a href="binop_1.html#K2">.</a> <font color="Maroon">vb</font>,<font color="Maroon">wa</font></span>)</span>
<b>by </b><i><a class="ref" href="bilinear.html#T27">BILINEAR:27</a></i>
<br/>.= 
<span class="p1">(<span class="default"><font color="Maroon">sc</font> <a href="binop_1.html#K2">.</a> <font color="Maroon">v1</font>,<font color="Maroon">w</font></span>)</span> <a href="rlvect_1.html#K4">+</a> <span class="p1">(<span class="default"><font color="Maroon">f</font> <a href="binop_1.html#K2">.</a> <font color="Maroon">vb</font>,<font color="Maroon">wa</font></span>)</span>
<b>by </b><i><a class="ref" href="hermitan.html#T25" target="_self">Th25</a>, <a class="ref" href="hermitan.html#T26" target="_self">Th26</a>, </i>
<br/>.= 
<span class="p1">(<span class="default"><font color="Maroon">sc</font> <a href="binop_1.html#K2">.</a> <font color="Maroon">v1</font>,<font color="Maroon">w</font></span>)</span> <a href="rlvect_1.html#K4">+</a> <span class="p1">(<span class="default"><font color="Maroon">sc</font> <a href="binop_1.html#K2">.</a> <font color="Maroon">v2</font>,<font color="Maroon">w</font></span>)</span>
<b>by </b><i><a class="ref" href="hermitan.html#T25" target="_self">Th25</a>, <a class="ref" href="hermitan.html#T28" target="_self">Th28</a>, </i>
<br/>.= 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="bilinear.html#K10">FunctionalSAF</a> <font color="Maroon">sc</font>,<font color="Maroon">w</font></span>)</span> <a href="funct_2.html#K3">.</a> <font color="Maroon">v1</font></span>)</span> <a href="rlvect_1.html#K4">+</a> <span class="p1">(<span class="default"><font color="Maroon">sc</font> <a href="binop_1.html#K2">.</a> <font color="Maroon">v2</font>,<font color="Maroon">w</font></span>)</span>
<b>by </b><i><a class="ref" href="bilinear.html#T10">BILINEAR:10</a></i>
<br/>.= 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="bilinear.html#K10">FunctionalSAF</a> <font color="Maroon">sc</font>,<font color="Maroon">w</font></span>)</span> <a href="funct_2.html#K3">.</a> <font color="Maroon">v1</font></span>)</span> <a href="rlvect_1.html#K4">+</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="bilinear.html#K10">FunctionalSAF</a> <font color="Maroon">sc</font>,<font color="Maroon">w</font></span>)</span> <a href="funct_2.html#K3">.</a> <font color="Maroon">v2</font></span>)</span>
<b>by </b><i><a class="ref" href="bilinear.html#T10">BILINEAR:10</a></i>
;<br/>


</div><b>end;</b></div>
<a NAME="E5:126_1_1"/><i><font color="Green">E132</font></i>: 
<font color="Maroon">sc</font> is <a href="hermitan.html#V3" target="_self">hermitan</a>
 
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="126_1_1_3"><b>proof </b></a><div class="add">

<b>let </b><font color="Maroon">v</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>, <font color="Maroon">w</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#D5" target="_self">HERMITAN:def 5</a><br/>

<b>reconsider </b><font color="Maroon">A</font> = <font color="Maroon">w</font> as   <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#K16">RKer</a> <span class="p3">(<span class="default"><font color="Maroon">f</font> <a href="hermitan.html#K3" target="_self">*'</a> </span>)</span></span>)</span></span>)</span> <b>by </b><i><a class="ref" href="hermitan.html#T18" target="_self">Th18</a></i>;<br/>
<b>consider </b><font color="Maroon">wa</font> being   <a href="vectsp_1.html#NM5">Vector</a> of <font color="Maroon">V</font><b> such that </b><br/><a NAME="E3:126_1_1_3"/><i><font color="Green">E133</font></i>: 
<font color="Maroon">A</font> <a href="hidden.html#R1">=</a> <font color="Maroon">wa</font> <a href="vectsp_4.html#K3">+</a> <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>
 <b>by </b><i><a class="ref" href="vectsp10.html#T23">VECTSP10:23</a></i>;<br/>
<b>reconsider </b><font color="Maroon">B</font> = <font color="Maroon">v</font> as   <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#K16">RKer</a> <span class="p3">(<span class="default"><font color="Maroon">f</font> <a href="hermitan.html#K3" target="_self">*'</a> </span>)</span></span>)</span></span>)</span> <b>by </b><i><a class="ref" href="hermitan.html#T18" target="_self">Th18</a></i>;<br/>
<b>consider </b><font color="Maroon">va</font> being   <a href="vectsp_1.html#NM5">Vector</a> of <font color="Maroon">V</font><b> such that </b><br/><a NAME="E6:126_1_1_3"/><i><font color="Green">E134</font></i>: 
<font color="Maroon">v</font> <a href="hidden.html#R1">=</a> <font color="Maroon">va</font> <a href="vectsp_4.html#K3">+</a> <span class="p1">(<span class="default"><a href="bilinear.html#K15">LKer</a> <font color="Maroon">f</font></span>)</span>
 <b>by </b><i><a class="ref" href="vectsp10.html#T23">VECTSP10:23</a></i>;<br/>
<a NAME="E7:126_1_1_3"/><i><font color="Green">E135</font></i>: 
<font color="Maroon">B</font> <a href="hidden.html#R1">=</a> <font color="Maroon">va</font> <a href="vectsp_4.html#K3">+</a> <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>
 
<b>by </b><i><a class="ref" href="hermitan.html#T28" target="_self">Th28</a>, <a class="ref" href="hermitan.html#T18" target="_self">Th18</a></i>;<br/>
<a NAME="E8:126_1_1_3"/><i><font color="Green">E136</font></i>: 
<font color="Maroon">w</font> <a href="hidden.html#R1">=</a> <font color="Maroon">wa</font> <a href="vectsp_4.html#K3">+</a> <span class="p1">(<span class="default"><a href="bilinear.html#K15">LKer</a> <font color="Maroon">f</font></span>)</span>
 
<b>by </b><i><a class="ref" href="hermitan.html#T26" target="_self">Th26</a>, <a class="ref" href="hermitan.html#T18" target="_self">Th18</a></i>;<br/>
<b>thus </b><font color="Maroon">sc</font> <a href="binop_1.html#K2">.</a> <font color="Maroon">v</font>,<font color="Maroon">w</font> = 
<font color="Maroon">f</font> <a href="binop_1.html#K2">.</a> <font color="Maroon">va</font>,<font color="Maroon">wa</font>
<b>by </b><i><a class="ref" href="hermitan.html#T26" target="_self">Th26</a>, <a class="ref" href="hermitan.html#T28" target="_self">Th28</a>, </i>
<br/>.= 
<span class="p1">(<span class="default"><font color="Maroon">f</font> <a href="binop_1.html#K2">.</a> <font color="Maroon">wa</font>,<font color="Maroon">va</font></span>)</span> <a href="complfld.html#K2">*'</a> 
<b>by </b><i/>
<br/>.= 
<span class="p1">(<span class="default"><font color="Maroon">sc</font> <a href="binop_1.html#K2">.</a> <font color="Maroon">w</font>,<font color="Maroon">v</font></span>)</span> <a href="complfld.html#K2">*'</a> 
<b>by </b><i>, , </i>
;<br/>


</div><b>end;</b></div>
<a NAME="E6:126_1_1"/>
<font color="Maroon">sc</font> is <a href="hermitan.html#V5" target="_self">diagReR+0valued</a>
 
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="126_1_1_4"><b>proof </b></a><div class="add">

<b>let </b><font color="Maroon">v</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#D7" target="_self">HERMITAN:def 7</a><br/>

<b>consider </b><font color="Maroon">va</font> being   <a href="vectsp_1.html#NM5">Vector</a> of <font color="Maroon">V</font><b> such that </b><br/><a NAME="E2:126_1_1_4"/><i><font color="Green">E184</font></i>: 
<font color="Maroon">v</font> <a href="hidden.html#R1">=</a> <font color="Maroon">va</font> <a href="vectsp_4.html#K3">+</a> <span class="p1">(<span class="default"><a href="bilinear.html#K15">LKer</a> <font color="Maroon">f</font></span>)</span>
 <b>by </b><i><a class="ref" href="vectsp10.html#T23">VECTSP10:23</a></i>;<br/>
<b>reconsider </b><font color="Maroon">A</font> = <font color="Maroon">v</font> as   <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#K16">RKer</a> <span class="p3">(<span class="default"><font color="Maroon">f</font> <a href="hermitan.html#K3" target="_self">*'</a> </span>)</span></span>)</span></span>)</span> <b>by </b><i><a class="ref" href="hermitan.html#T18" target="_self">Th18</a></i>;<br/>
<a NAME="E4:126_1_1_4"/>
<font color="Maroon">A</font> <a href="hidden.html#R1">=</a> <font color="Maroon">va</font> <a href="vectsp_4.html#K3">+</a> <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>
 
<b>by </b><i><a class="ref" href="hermitan.html#T26" target="_self">Th26</a>, <a class="ref" href="hermitan.html#T18" target="_self">Th18</a></i>;<br/>
<a NAME="E5:126_1_1_4"/><b>then </b>
<font color="Maroon">sc</font> <a href="binop_1.html#K2">.</a> <font color="Maroon">v</font>,<font color="Maroon">v</font> <a href="hidden.html#R1">=</a> <font color="Maroon">f</font> <a href="binop_1.html#K2">.</a> <font color="Maroon">va</font>,<font color="Maroon">va</font>
 
<b>by </b><i><a class="ref" href="hermitan.html#T26" target="_self">Th26</a>, </i>;<br/>
<b>hence </b><a NAME="E6:126_1_1_4"/>
0 <a href="xxreal_0.html#R1">&lt;=</a>  <a href="complex1.html#K3">Re</a> <span class="p1">(<span class="default"><font color="Maroon">sc</font> <a href="binop_1.html#K2">.</a> <font color="Maroon">v</font>,<font color="Maroon">v</font></span>)</span>
 <b>by </b><i/>;<br/>


</div><b>end;</b></div>
<b>hence </b><a NAME="E7:126_1_1"/>
 <a href="hermitan.html#K8" target="_self">Q*Form</a> <font color="Maroon">f</font> is  <a href="hermitan.html#V5" target="_self">diagReR+0valued</a> <a href="hermitan.html#NM3">hermitan-Form</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>
 <b>by </b><i><a class="ref" href="hermitan.html#T21" target="_self">Th21</a>, <a class="ref" href="hermitan.html#T22" target="_self">Th22</a>, <a class="ref" href="hermitan.html#T25" target="_self">Th25</a></i>;<br/>


</div>
