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<b>let </b><font color="Maroon" title="c1">n</font> be   <a href="nat_1.html#NM1" title="NAT_1:NM.1">Nat</a>;<br/><b>let </b><font color="Maroon" title="c2">K</font> be   <a href="vectsp_1.html#NM2" title="VECTSP_1:NM.2">Field</a>;<br/><b>let </b><font color="Maroon" title="c3">M1</font>, <font color="Maroon" title="c4">M2</font> be   <a href="matrix_1.html#NM5" title="MATRIX_1:NM.5">Matrix</a> of <font color="Maroon" title="c1">n</font>,<font color="Maroon" title="c2">K</font>;<br/>







<b>assume </b><a NAME="E1:55"/><i><font color="Green" title="E23">A1</font></i>: 
( <font color="Maroon" title="c3">M1</font> is <a href="matrix_6.html#V4" title="MATRIX_6:attr.4">Orthogonal</a> &amp; <font color="Maroon" title="c3">M1</font> <a href="matrix_6.html#R1" title="MATRIX_6:pred.1">commutes_with</a> <font color="Maroon" title="c4">M2</font> )
 ;<br/>

<a NAME="E2:55"/><b>then </b>
( <font color="Maroon" title="c3">M1</font> <a href="matrix_1.html#K5" title="MATRIX_1:func.5">@</a>  <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c3">M1</font> <a href="matrix_6.html#K5" title="MATRIX_6:func.5">~</a>  &amp; <font color="Maroon" title="c3">M1</font> is <a href="matrix_6.html#V1" title="MATRIX_6:attr.1">invertible</a> )
 
<b>by </b><i><a class="ref" href="matrix_6.html#D7" target="_self" title="MATRIX_6:def.7">Def7</a></i>;<br/>
<b>hence </b><a NAME="E3:55"/>
<font color="Maroon" title="c3">M1</font> <a href="matrix_1.html#K5" title="MATRIX_1:func.5">@</a>  <a href="matrix_6.html#R1" title="MATRIX_6:pred.1">commutes_with</a> <font color="Maroon" title="c4">M2</font>
 <b>by </b><i><a class="txt" href="matrix_6.html#E1:55"><i><font color="Green" title="E23">A1</font></i></a>, <a class="ref" href="matrix_6.html#T41" target="_self" title="MATRIX_6:th.41">Th41</a></i>;<br/>


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