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

<b>let </b><font color="Maroon">n</font> be   <a href="nat_1.html#NM1">Nat</a>;<br/><b>let </b><font color="Maroon">K</font> be   <a href="vectsp_1.html#NM2">Field</a>;<br/><b>let </b><font color="Maroon">M1</font> be   <a href="matrix_1.html#NM5">Matrix</a> of <font color="Maroon">n</font>,<font color="Maroon">K</font>;<br/>





<b>assume </b><a NAME="E1:16"/><i><font color="Green">E36</font></i>: 
( <font color="Maroon">M1</font> is <a href="matrix_8.html#V1" target="_self">Idempotent</a> &amp; <font color="Maroon">M1</font> is <a href="matrix_6.html#V4">Orthogonal</a> )
 ;<br/>

<a NAME="E2:16"/>
( <font color="Maroon">M1</font> is <a href="matrix_6.html#V1">invertible</a> &amp; <font color="Maroon">M1</font> <a href="matrix_1.html#K5">@</a>  <a href="hidden.html#R1">=</a> <font color="Maroon">M1</font> <a href="matrix_6.html#K5">~</a>  )
 
<b>by </b><i>, <a class="ref" href="matrix_6.html#D7">MATRIX_6:def 7</a></i>;<br/>
<a NAME="E3:16"/><b>then </b>
<font color="Maroon">M1</font> <a href="hidden.html#R1">=</a>  <a href="matrix_1.html#K12">1.</a> <font color="Maroon">K</font>,<font color="Maroon">n</font>
 
<b>by </b><i>, </i>;<br/>
<b>hence </b><a NAME="E4:16"/>
<font color="Maroon">M1</font> is <a href="matrix_6.html#V2">symmetric</a>
 ;<br/>


</div>
