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<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>let </b><font color="Maroon">M2</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="E1:55"/><i><font color="Green">E35</font></i>: 
( <font color="Maroon">M1</font> is <a href="matrix_6.html#V4" target="_self">Orthogonal</a> &amp; <font color="Maroon">M1</font> <a href="matrix_6.html#R1" target="_self">commutes_with</a> <font color="Maroon">M2</font> )
 ;<br/>

<a NAME="E2:55"/><b>then </b>
( <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" target="_self">~</a>  &amp; <font color="Maroon">M1</font> is <a href="matrix_6.html#V1" target="_self">invertible</a> )
 
<b>by </b><i/>;<br/>
<b>hence </b><a NAME="E3:55"/>
<font color="Maroon">M1</font> <a href="matrix_1.html#K5">@</a>  <a href="matrix_6.html#R1" target="_self">commutes_with</a> <font color="Maroon">M2</font>
 <b>by </b><i>, </i>;<br/>


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