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<b>let </b><font color="Maroon" title="c1">K</font> be   <a href="vectsp_1.html#NM3" title="VECTSP_1:NM.3">Field</a>; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> for <font color="Olive" title="b1">V</font> being non <a href="struct_0.html#V7" title="STRUCT_0:attr.7">trivial</a> <a href="vectsp_1.html#NM7" title="VECTSP_1:NM.7">VectSp</a> of <font color="Maroon" title="c1">K</font> holds <br/> (  <a href="matrlin2.html#K7" title="MATRLIN2:func.7">id</a> <font color="Olive" title="b1">V</font> is <a href="vectsp11.html#V1" title="VECTSP11:attr.1">with_eigenvalues</a> &amp;  <a href="group_1.html#K1" title="GROUP_1:func.1">1_</a> <font color="Maroon" title="c1">K</font> is    <a href="vectsp11.html#M1" title="VECTSP11:mode.1">eigenvalue</a> of  <a href="matrlin2.html#K7" title="MATRLIN2:func.7">id</a> <font color="Olive" title="b1">V</font> &amp; ( for <font color="Olive" title="b2">v</font> being  <a href="vectsp_1.html#NM6" title="VECTSP_1:NM.6">Vector</a> of <font color="Olive" title="b1">V</font> holds  <font color="Olive" title="b2">v</font> is    <a href="vectsp11.html#M2" title="VECTSP11:mode.2">eigenvector</a> of  <a href="matrlin2.html#K7" title="MATRLIN2:func.7">id</a> <font color="Olive" title="b1">V</font>, <a href="group_1.html#K1" title="GROUP_1:func.1">1_</a> <font color="Maroon" title="c1">K</font> ) )</span><br/><b>let </b><font color="Maroon" title="c2">V</font> be  non <a href="struct_0.html#V7" title="STRUCT_0:attr.7">trivial</a> <a href="vectsp_1.html#NM7" title="VECTSP_1:NM.7">VectSp</a> of <font color="Maroon" title="c1">K</font>; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> (  <a href="matrlin2.html#K7" title="MATRLIN2:func.7">id</a> <font color="Maroon" title="c2">V</font> is <a href="vectsp11.html#V1" title="VECTSP11:attr.1">with_eigenvalues</a> &amp;  <a href="group_1.html#K1" title="GROUP_1:func.1">1_</a> <font color="Maroon" title="c1">K</font> is    <a href="vectsp11.html#M1" title="VECTSP11:mode.1">eigenvalue</a> of  <a href="matrlin2.html#K7" title="MATRLIN2:func.7">id</a> <font color="Maroon" title="c2">V</font> &amp; ( for <font color="Olive" title="b1">v</font> being  <a href="vectsp_1.html#NM6" title="VECTSP_1:NM.6">Vector</a> of <font color="Maroon" title="c2">V</font> holds  <font color="Olive" title="b1">v</font> is    <a href="vectsp11.html#M2" title="VECTSP11:mode.2">eigenvector</a> of  <a href="matrlin2.html#K7" title="MATRLIN2:func.7">id</a> <font color="Maroon" title="c2">V</font>, <a href="group_1.html#K1" title="GROUP_1:func.1">1_</a> <font color="Maroon" title="c1">K</font> ) )</span><br/>



<b>thus </b><a NAME="E1:18"/><i><font color="Green" title="E15">A1</font></i>: 
 <a href="matrlin2.html#K7" title="MATRLIN2:func.7">id</a> <font color="Maroon" title="c2">V</font> is <a href="vectsp11.html#V1" title="VECTSP11:attr.1">with_eigenvalues</a>
 <b>by </b><i><a class="txt" href="vectsp11.html#E11"><i><font color="Green" title="E11">Lm2</font></i></a></i>; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> (  <a href="group_1.html#K1" title="GROUP_1:func.1">1_</a> <font color="Maroon" title="c1">K</font> is    <a href="vectsp11.html#M1" title="VECTSP11:mode.1">eigenvalue</a> of  <a href="matrlin2.html#K7" title="MATRLIN2:func.7">id</a> <font color="Maroon" title="c2">V</font> &amp; ( for <font color="Olive" title="b1">v</font> being  <a href="vectsp_1.html#NM6" title="VECTSP_1:NM.6">Vector</a> of <font color="Maroon" title="c2">V</font> holds  <font color="Olive" title="b1">v</font> is    <a href="vectsp11.html#M2" title="VECTSP11:mode.2">eigenvector</a> of  <a href="matrlin2.html#K7" title="MATRLIN2:func.7">id</a> <font color="Maroon" title="c2">V</font>, <a href="group_1.html#K1" title="GROUP_1:func.1">1_</a> <font color="Maroon" title="c1">K</font> ) )</span><br/>

<b>consider </b><font color="Maroon" title="c3">v</font> being   <a href="vectsp_1.html#NM6" title="VECTSP_1:NM.6">Vector</a> of <font color="Maroon" title="c2">V</font><b> such that </b><br/><a NAME="E3:18"/><i><font color="Green" title="E16">A2</font></i>: 
( <font color="Maroon" title="c3">v</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a>  <a href="struct_0.html#K4" title="STRUCT_0:func.4">0.</a> <font color="Maroon" title="c2">V</font> &amp; <span class="p1">(<span class="default"><a href="matrlin2.html#K7" title="MATRLIN2:func.7">id</a> <font color="Maroon" title="c2">V</font></span>)</span> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c3">v</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><a href="group_1.html#K1" title="GROUP_1:func.1">1_</a> <font color="Maroon" title="c1">K</font></span>)</span> <a href="vectsp_1.html#K4" title="VECTSP_1:func.4">*</a> <font color="Maroon" title="c3">v</font> )
 <b>by </b><i><a class="txt" href="vectsp11.html#E11"><i><font color="Green" title="E11">Lm2</font></i></a></i>;<br/>
<b>thus </b><a NAME="E4:18"/><i><font color="Green" title="E17">A3</font></i>: 
 <a href="group_1.html#K1" title="GROUP_1:func.1">1_</a> <font color="Maroon" title="c1">K</font> is    <a href="vectsp11.html#M1" title="VECTSP11:mode.1">eigenvalue</a> of  <a href="matrlin2.html#K7" title="MATRLIN2:func.7">id</a> <font color="Maroon" title="c2">V</font>
 <b>by </b><i><a class="txt" href="#E1:18"><i><font color="Green" title="E15">A1</font></i></a>, <a class="txt" href="#E3:18"><i><font color="Green" title="E16">A2</font></i></a>, <a class="ref" href="vectsp11.html#D2" target="_self" title="VECTSP11:def.2">Def2</a></i>; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> for <font color="Olive" title="b1">v</font> being  <a href="vectsp_1.html#NM6" title="VECTSP_1:NM.6">Vector</a> of <font color="Maroon" title="c2">V</font> holds  <font color="Olive" title="b1">v</font> is    <a href="vectsp11.html#M2" title="VECTSP11:mode.2">eigenvector</a> of  <a href="matrlin2.html#K7" title="MATRLIN2:func.7">id</a> <font color="Maroon" title="c2">V</font>, <a href="group_1.html#K1" title="GROUP_1:func.1">1_</a> <font color="Maroon" title="c1">K</font></span><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">V</font>; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> <font color="Maroon" title="c4">w</font> is    <a href="vectsp11.html#M2" title="VECTSP11:mode.2">eigenvector</a> of  <a href="matrlin2.html#K7" title="MATRLIN2:func.7">id</a> <font color="Maroon" title="c2">V</font>, <a href="group_1.html#K1" title="GROUP_1:func.1">1_</a> <font color="Maroon" title="c1">K</font></span><br/>

<span class="p1">(<span class="default"><a href="matrlin2.html#K7" title="MATRLIN2:func.7">id</a> <font color="Maroon" title="c2">V</font></span>)</span> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c4">w</font> = 
<font color="Maroon" title="c4">w</font>
<b>by </b><i><a class="ref" href="funct_1.html#T34" title="FUNCT_1:th.34">FUNCT_1:34</a></i>
<br/>.= 
<span class="p1">(<span class="default"><a href="group_1.html#K1" title="GROUP_1:func.1">1_</a> <font color="Maroon" title="c1">K</font></span>)</span> <a href="vectsp_1.html#K4" title="VECTSP_1:func.4">*</a> <font color="Maroon" title="c4">w</font>
<b>by </b><i><a class="ref" href="vectsp_1.html#D26" title="VECTSP_1:def.26">VECTSP_1:def 26</a></i>
;<br/>
<b>hence </b><a NAME="E6:18"/>
<font color="Maroon" title="c4">w</font> is    <a href="vectsp11.html#M2" title="VECTSP11:mode.2">eigenvector</a> of  <a href="matrlin2.html#K7" title="MATRLIN2:func.7">id</a> <font color="Maroon" title="c2">V</font>, <a href="group_1.html#K1" title="GROUP_1:func.1">1_</a> <font color="Maroon" title="c1">K</font>
 <b>by </b><i><a class="txt" href="#E1:18"><i><font color="Green" title="E15">A1</font></i></a>, <a class="txt" href="#E4:18"><i><font color="Green" title="E17">A3</font></i></a>, <a class="ref" href="vectsp11.html#D3" target="_self" title="VECTSP11:def.3">Def3</a></i>; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> verum</span><br/>


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