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

<b>consider </b><font color="Maroon">f</font> being  <a href="funct_1.html#V3">V6</a> non <a href="realset1.html#V1">trivial</a> <a href="hahnban1.html#NM2">linear-Functional</a> of <font color="Maroon">V</font>;<br/>
<b>take </b><font color="Maroon">ff</font> =  <a href="bilinear.html#K11" target="_self">FormFunctional</a> <font color="Maroon">f</font>,<font color="Maroon">f</font>;<br/>

<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="134_1_1_1"><b>now </b></a><div class="add"><b>let </b><font color="Maroon">v</font> be   <a href="vectsp_1.html#NM5">Vector</a> of <font color="Maroon">V</font>, <font color="Maroon">w</font> be   <a href="vectsp_1.html#NM5">Vector</a> of <font color="Maroon">V</font>;<br/><b>thus </b><font color="Maroon">ff</font> <a href="binop_1.html#K2">.</a> <font color="Maroon">v</font>,<font color="Maroon">w</font> = 
<span class="p1">(<span class="default"><font color="Maroon">f</font> <a href="funct_2.html#K3">.</a> <font color="Maroon">v</font></span>)</span> <a href="group_1.html#K10">*</a> <span class="p1">(<span class="default"><font color="Maroon">f</font> <a href="funct_2.html#K3">.</a> <font color="Maroon">w</font></span>)</span>
<b>by </b><i/>
<br/>.= 
<font color="Maroon">ff</font> <a href="binop_1.html#K2">.</a> <font color="Maroon">w</font>,<font color="Maroon">v</font>
<b>by </b><i/>
;<br/></div><b>end;</b></div>
<b>hence </b><a NAME="E3:134_1_1"/>
( <font color="Maroon">ff</font> is <a href="bilinear.html#V7" target="_self">symmetric</a> &amp; not <font color="Maroon">ff</font> is <a href="realset1.html#V1">trivial</a> &amp; not <font color="Maroon">ff</font> is <a href="funct_1.html#V3">constant</a> &amp; <font color="Maroon">ff</font> is <a href="bilinear.html#V1" target="_self">additiveFAF</a> &amp; <font color="Maroon">ff</font> is <a href="bilinear.html#V3" target="_self">homogeneousFAF</a> &amp; <font color="Maroon">ff</font> is <a href="bilinear.html#V2" target="_self">additiveSAF</a> &amp; <font color="Maroon">ff</font> is <a href="bilinear.html#V4" target="_self">homogeneousSAF</a> )
 <b>by </b><i><a class="ref" href="bilinear.html#D11" target="_self">Def11</a></i>;<br/>


</div>
