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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>; <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">K</font> being  <a href="vectsp_1.html#NM3" title="VECTSP_1:NM.3">Field</a><br/> for <font color="Olive" title="b2">M4</font>, <font color="Olive" title="b3">M2</font> being  <a href="matrix_1.html#NM5" title="MATRIX_1:NM.5">Matrix</a> of <font color="Maroon" title="c1">n</font>,<font color="Olive" title="b1">K</font>  st <font color="Olive" title="b2">M4</font> is <a href="matrix_6.html#V4" title="MATRIX_6:attr.4">Orthogonal</a> holds <br/><span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Olive" title="b2">M4</font> <a href="matrix_1.html#K5" title="MATRIX_1:func.5">@</a> </span>)</span> <a href="matrix_6.html#K4" title="MATRIX_6:func.4">*</a> <font color="Olive" title="b3">M2</font></span>)</span> <a href="matrix_6.html#K4" title="MATRIX_6:func.4">*</a> <font color="Olive" title="b2">M4</font> <a href="matrix_8.html#R1" title="MATRIX_8:pred.1">is_similar_to</a> <font color="Olive" title="b3">M2</font></span><br/><b>let </b><font color="Maroon" title="c2">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">M4</font>, <font color="Olive" title="b2">M2</font> being  <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>  st <font color="Olive" title="b1">M4</font> is <a href="matrix_6.html#V4" title="MATRIX_6:attr.4">Orthogonal</a> holds <br/><span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Olive" title="b1">M4</font> <a href="matrix_1.html#K5" title="MATRIX_1:func.5">@</a> </span>)</span> <a href="matrix_6.html#K4" title="MATRIX_6:func.4">*</a> <font color="Olive" title="b2">M2</font></span>)</span> <a href="matrix_6.html#K4" title="MATRIX_6:func.4">*</a> <font color="Olive" title="b1">M4</font> <a href="matrix_8.html#R1" title="MATRIX_8:pred.1">is_similar_to</a> <font color="Olive" title="b2">M2</font></span><br/><b>let </b><font color="Maroon" title="c3">M4</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>; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> ( <font color="Maroon" title="c3">M4</font> is <a href="matrix_6.html#V4" title="MATRIX_6:attr.4">Orthogonal</a> implies <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c3">M4</font> <a href="matrix_1.html#K5" title="MATRIX_1:func.5">@</a> </span>)</span> <a href="matrix_6.html#K4" title="MATRIX_6:func.4">*</a> <font color="Maroon" title="c4">M2</font></span>)</span> <a href="matrix_6.html#K4" title="MATRIX_6:func.4">*</a> <font color="Maroon" title="c3">M4</font> <a href="matrix_8.html#R1" title="MATRIX_8:pred.1">is_similar_to</a> <font color="Maroon" title="c4">M2</font> )</span><br/>







<b>assume </b><a NAME="E1:55"/><i><font color="Green" title="E11">A1</font></i>: 
<font color="Maroon" title="c3">M4</font> is <a href="matrix_6.html#V4" title="MATRIX_6:attr.4">Orthogonal</a>
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c3">M4</font> <a href="matrix_1.html#K5" title="MATRIX_1:func.5">@</a> </span>)</span> <a href="matrix_6.html#K4" title="MATRIX_6:func.4">*</a> <font color="Maroon" title="c4">M2</font></span>)</span> <a href="matrix_6.html#K4" title="MATRIX_6:func.4">*</a> <font color="Maroon" title="c3">M4</font> <a href="matrix_8.html#R1" title="MATRIX_8:pred.1">is_similar_to</a> <font color="Maroon" title="c4">M2</font></span><br/>

<b>take </b>
<font color="Maroon" title="c3">M4</font>
; <i><font color="Red">:: according to </font></i><a class="ref" href="matrix_8.html#D5" target="_self" title="MATRIX_8:def.5">MATRIX_8:def 5</a> <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> ( <font color="Maroon" title="c3">M4</font> is <a href="matrix_6.html#V1" title="MATRIX_6:attr.1">invertible</a> &amp; <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c3">M4</font> <a href="matrix_1.html#K5" title="MATRIX_1:func.5">@</a> </span>)</span> <a href="matrix_6.html#K4" title="MATRIX_6:func.4">*</a> <font color="Maroon" title="c4">M2</font></span>)</span> <a href="matrix_6.html#K4" title="MATRIX_6:func.4">*</a> <font color="Maroon" title="c3">M4</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c3">M4</font> <a href="matrix_6.html#K5" title="MATRIX_6:func.5">~</a> </span>)</span> <a href="matrix_6.html#K4" title="MATRIX_6:func.4">*</a> <font color="Maroon" title="c4">M2</font></span>)</span> <a href="matrix_6.html#K4" title="MATRIX_6:func.4">*</a> <font color="Maroon" title="c3">M4</font> )</span><br/>

<b>thus </b><a NAME="E2:55"/>
( <font color="Maroon" title="c3">M4</font> is <a href="matrix_6.html#V1" title="MATRIX_6:attr.1">invertible</a> &amp; <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c3">M4</font> <a href="matrix_1.html#K5" title="MATRIX_1:func.5">@</a> </span>)</span> <a href="matrix_6.html#K4" title="MATRIX_6:func.4">*</a> <font color="Maroon" title="c4">M2</font></span>)</span> <a href="matrix_6.html#K4" title="MATRIX_6:func.4">*</a> <font color="Maroon" title="c3">M4</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c3">M4</font> <a href="matrix_6.html#K5" title="MATRIX_6:func.5">~</a> </span>)</span> <a href="matrix_6.html#K4" title="MATRIX_6:func.4">*</a> <font color="Maroon" title="c4">M2</font></span>)</span> <a href="matrix_6.html#K4" title="MATRIX_6:func.4">*</a> <font color="Maroon" title="c3">M4</font> )
 <b>by </b><i><a class="txt" href="#E1:55"><i><font color="Green" title="E11">A1</font></i></a>, <a class="ref" href="matrix_6.html#D7" title="MATRIX_6:def.7">MATRIX_6:def 7</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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