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<b>let </b><font color="Maroon" title="c1">V</font>, <font color="Maroon" title="c2">W</font> be  non <a href="struct_0.html#V2" title="STRUCT_0:attr.2">empty</a>  <a href="vectsp_1.html#L1" title="VECTSP_1:struct.1">VectSpStr</a> of  <a href="complfld.html#K1" title="COMPLFLD:func.1">F_Complex</a> ;<br/><b>let </b><font color="Maroon" title="c3">v1</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>let </b><font color="Maroon" title="c4">w</font> be   <a href="vectsp_1.html#NM6" title="VECTSP_1:NM.6">Vector</a> of <font color="Maroon" title="c2">W</font>;<br/><b>let </b><font color="Maroon" title="c5">r</font> be   <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <a href="complfld.html#K1" title="COMPLFLD:func.1">F_Complex</a> ;<br/><b>let </b><font color="Maroon" title="c6">f</font> be   <a href="bilinear.html#NM1" title="BILINEAR:NM.1">Form</a> of <font color="Maroon" title="c1">V</font>,<font color="Maroon" title="c2">W</font>;<br/>









<b>set </b><font color="Maroon" title="c7">F</font> =  <a href="bilinear.html#K9" title="BILINEAR:func.9">FunctionalFAF</a> <font color="Maroon" title="c6">f</font>,<font color="Maroon" title="c3">v1</font>;<br/>
<b>assume </b><a NAME="E1:44"/>
<font color="Maroon" title="c6">f</font> is <a href="hermitan.html#V2" title="HERMITAN:attr.2">cmplxhomogeneousFAF</a>
 ;<br/>

<a NAME="E2:44"/><b>then </b><i><font color="Green" title="E23">A1</font></i>: 
 <a href="bilinear.html#K9" title="BILINEAR:func.9">FunctionalFAF</a> <font color="Maroon" title="c6">f</font>,<font color="Maroon" title="c3">v1</font> is <a href="hermitan.html#V1" title="HERMITAN:attr.1">cmplxhomogeneous</a>
 
<b>by </b><i><a class="ref" href="hermitan.html#D4" target="_self" title="HERMITAN:def.4">Def4</a></i>;<br/>
<b>thus </b><font color="Maroon" title="c6">f</font> <a href="binop_1.html#K2" title="BINOP_1:func.2">.</a> <font color="Maroon" title="c3">v1</font>,<span class="p1">(<span class="default"><font color="Maroon" title="c5">r</font> <a href="vectsp_1.html#K4" title="VECTSP_1:func.4">*</a> <font color="Maroon" title="c4">w</font></span>)</span> = 
<span class="p1">(<span class="default"><a href="bilinear.html#K9" title="BILINEAR:func.9">FunctionalFAF</a> <font color="Maroon" title="c6">f</font>,<font color="Maroon" title="c3">v1</font></span>)</span> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <span class="p1">(<span class="default"><font color="Maroon" title="c5">r</font> <a href="vectsp_1.html#K4" title="VECTSP_1:func.4">*</a> <font color="Maroon" title="c4">w</font></span>)</span>
<b>by </b><i><a class="ref" href="bilinear.html#T9" title="BILINEAR:th.9">BILINEAR:9</a></i>
<br/>.= 
<span class="p1">(<span class="default"><font color="Maroon" title="c5">r</font> <a href="complfld.html#K2" title="COMPLFLD:func.2">*'</a> </span>)</span> <a href="group_1.html#K9" title="GROUP_1:func.9">*</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="bilinear.html#K9" title="BILINEAR:func.9">FunctionalFAF</a> <font color="Maroon" title="c6">f</font>,<font color="Maroon" title="c3">v1</font></span>)</span> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c4">w</font></span>)</span>
<b>by </b><i><a class="txt" href="hermitan.html#E2:44"><i><font color="Green" title="E23">A1</font></i></a>, <a class="ref" href="hermitan.html#D1" target="_self" title="HERMITAN:def.1">Def1</a></i>
<br/>.= 
<span class="p1">(<span class="default"><font color="Maroon" title="c5">r</font> <a href="complfld.html#K2" title="COMPLFLD:func.2">*'</a> </span>)</span> <a href="group_1.html#K9" title="GROUP_1:func.9">*</a> <span class="p1">(<span class="default"><font color="Maroon" title="c6">f</font> <a href="binop_1.html#K2" title="BINOP_1:func.2">.</a> <font color="Maroon" title="c3">v1</font>,<font color="Maroon" title="c4">w</font></span>)</span>
<b>by </b><i><a class="ref" href="bilinear.html#T9" title="BILINEAR:th.9">BILINEAR:9</a></i>
;<br/>


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