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<b>consider </b><font color="Maroon" title="c3">f</font> being  <a href="funct_1.html#V3" title="FUNCT_1:attr.3">V7</a> non <a href="realset1.html#V1" title="REALSET1:attr.1">trivial</a> <a href="hahnban1.html#NM2" title="HAHNBAN1:NM.2">linear-Functional</a> of <font color="Maroon" title="c2">V</font>;<br/>
<b>take </b><font color="Maroon" title="c4">ff</font> =  <a href="bilinear.html#K11" title="BILINEAR:func.11">FormFunctional</a> <font color="Maroon" title="c3">f</font>,<font color="Maroon" title="c3">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" title="c5">v</font>, <font color="Maroon" title="c6">w</font> be   <a href="vectsp_1.html#NM6" title="VECTSP_1:NM.6">Vector</a> of <font color="Maroon" title="c2">V</font>;<br/><b>thus </b><font color="Maroon" title="c4">ff</font> <a href="binop_1.html#K2" title="BINOP_1:func.2">.</a> <font color="Maroon" title="c5">v</font>,<font color="Maroon" title="c6">w</font> = 
<span class="p1">(<span class="default"><font color="Maroon" title="c3">f</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c5">v</font></span>)</span> <a href="group_1.html#K9" title="GROUP_1:func.9">*</a> <span class="p1">(<span class="default"><font color="Maroon" title="c3">f</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c6">w</font></span>)</span>
<b>by </b><i><a class="ref" href="bilinear.html#D11" target="_self" title="BILINEAR:def.11">Def11</a></i>
<br/>.= 
<font color="Maroon" title="c4">ff</font> <a href="binop_1.html#K2" title="BINOP_1:func.2">.</a> <font color="Maroon" title="c6">w</font>,<font color="Maroon" title="c5">v</font>
<b>by </b><i><a class="ref" href="bilinear.html#D11" target="_self" title="BILINEAR:def.11">Def11</a></i>
;<br/></div><b>end;</b></div>
<b>hence </b><a NAME="E3:134_1_1"/>
( <font color="Maroon" title="c4">ff</font> is <a href="bilinear.html#V7" title="BILINEAR:attr.7">symmetric</a> &amp; not <font color="Maroon" title="c4">ff</font> is <a href="realset1.html#V1" title="REALSET1:attr.1">trivial</a> &amp; not <font color="Maroon" title="c4">ff</font> is <a href="funct_1.html#V3" title="FUNCT_1:attr.3">constant</a> &amp; <font color="Maroon" title="c4">ff</font> is <a href="bilinear.html#V1" title="BILINEAR:attr.1">additiveFAF</a> &amp; <font color="Maroon" title="c4">ff</font> is <a href="bilinear.html#V3" title="BILINEAR:attr.3">homogeneousFAF</a> &amp; <font color="Maroon" title="c4">ff</font> is <a href="bilinear.html#V2" title="BILINEAR:attr.2">additiveSAF</a> &amp; <font color="Maroon" title="c4">ff</font> is <a href="bilinear.html#V4" title="BILINEAR:attr.4">homogeneousSAF</a> )
 <b>by </b><i><a class="ref" href="bilinear.html#D26" target="_self" title="BILINEAR:def.26">Def26</a></i>;<br/>


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