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<span class="kw">let </span><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:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> for <font color="Olive" title="b1">K</font> being  <a href="polynom5.html#V2" title="POLYNOM5:attr.2">algebraic-closed</a>  <a href="vectsp_1.html#NM3" title="VECTSP_1:NM.3">Field</a><br/> for <font color="Olive" title="b2">M</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>  ex <font color="Olive" title="b3">J</font> being  <a href="relat_1.html#V2" title="RELAT_1:attr.2">non-empty</a>  <a href="matrixj2.html#NM1" title="MATRIXJ2:NM.1">FinSequence_of_Jordan_block</a> of <font color="Olive" title="b1">K</font> ex <font color="Olive" title="b4">P</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 <br/>(  <a href="wsierp_1.html#K3" title="WSIERP_1:func.3">Sum</a> <span class="p1">(<span class="default"><a href="matrixj1.html#K10" title="MATRIXJ1:func.10">Len</a> <font color="Olive" title="b3">J</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c1">n</font> &amp; <font color="Olive" title="b4">P</font> is  <a href="matrix_6.html#V1" title="MATRIX_6:attr.1">invertible</a>  &amp; <font color="Olive" title="b2">M</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><font color="Olive" title="b4">P</font> <a href="matrix_3.html#K4" title="MATRIX_3:func.4">*</a> <span class="p2">(<span class="default"><a href="matrixj1.html#K20" title="MATRIXJ1:func.20">block_diagonal</a> <font color="Olive" title="b3">J</font>,<span class="p3">(<span class="default"><a href="struct_0.html#K4" title="STRUCT_0:func.4">0.</a> <font color="Olive" title="b1">K</font></span>)</span></span>)</span></span>)</span> <a href="matrix_3.html#K4" title="MATRIX_3:func.4">*</a> <span class="p1">(<span class="default"><font color="Olive" title="b4">P</font> <a href="matrix_6.html#K5" title="MATRIX_6:func.5">~</a> </span>)</span> )</span><br/><span class="kw">let </span><font color="Maroon" title="c2">K</font> be   <a href="polynom5.html#V2" title="POLYNOM5:attr.2">algebraic-closed</a>  <a href="vectsp_1.html#NM3" title="VECTSP_1:NM.3">Field</a>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> for <font color="Olive" title="b1">M</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>  ex <font color="Olive" title="b2">J</font> being  <a href="relat_1.html#V2" title="RELAT_1:attr.2">non-empty</a>  <a href="matrixj2.html#NM1" title="MATRIXJ2:NM.1">FinSequence_of_Jordan_block</a> of <font color="Maroon" title="c2">K</font> ex <font color="Olive" title="b3">P</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 <br/>(  <a href="wsierp_1.html#K3" title="WSIERP_1:func.3">Sum</a> <span class="p1">(<span class="default"><a href="matrixj1.html#K10" title="MATRIXJ1:func.10">Len</a> <font color="Olive" title="b2">J</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c1">n</font> &amp; <font color="Olive" title="b3">P</font> is  <a href="matrix_6.html#V1" title="MATRIX_6:attr.1">invertible</a>  &amp; <font color="Olive" title="b1">M</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><font color="Olive" title="b3">P</font> <a href="matrix_3.html#K4" title="MATRIX_3:func.4">*</a> <span class="p2">(<span class="default"><a href="matrixj1.html#K20" title="MATRIXJ1:func.20">block_diagonal</a> <font color="Olive" title="b2">J</font>,<span class="p3">(<span class="default"><a href="struct_0.html#K4" title="STRUCT_0:func.4">0.</a> <font color="Maroon" title="c2">K</font></span>)</span></span>)</span></span>)</span> <a href="matrix_3.html#K4" title="MATRIX_3:func.4">*</a> <span class="p1">(<span class="default"><font color="Olive" title="b3">P</font> <a href="matrix_6.html#K5" title="MATRIX_6:func.5">~</a> </span>)</span> )</span><br/><span class="kw">let </span><font color="Maroon" title="c3">M</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:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide">  ex <font color="Olive" title="b1">J</font> being  <a href="relat_1.html#V2" title="RELAT_1:attr.2">non-empty</a>  <a href="matrixj2.html#NM1" title="MATRIXJ2:NM.1">FinSequence_of_Jordan_block</a> of <font color="Maroon" title="c2">K</font> ex <font color="Olive" title="b2">P</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 <br/>(  <a href="wsierp_1.html#K3" title="WSIERP_1:func.3">Sum</a> <span class="p1">(<span class="default"><a href="matrixj1.html#K10" title="MATRIXJ1:func.10">Len</a> <font color="Olive" title="b1">J</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c1">n</font> &amp; <font color="Olive" title="b2">P</font> is  <a href="matrix_6.html#V1" title="MATRIX_6:attr.1">invertible</a>  &amp; <font color="Maroon" title="c3">M</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><font color="Olive" title="b2">P</font> <a href="matrix_3.html#K4" title="MATRIX_3:func.4">*</a> <span class="p2">(<span class="default"><a href="matrixj1.html#K20" title="MATRIXJ1:func.20">block_diagonal</a> <font color="Olive" title="b1">J</font>,<span class="p3">(<span class="default"><a href="struct_0.html#K4" title="STRUCT_0:func.4">0.</a> <font color="Maroon" title="c2">K</font></span>)</span></span>)</span></span>)</span> <a href="matrix_3.html#K4" title="MATRIX_3:func.4">*</a> <span class="p1">(<span class="default"><font color="Olive" title="b2">P</font> <a href="matrix_6.html#K5" title="MATRIX_6:func.5">~</a> </span>)</span> )</span><br/>





<div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="54_1"><span class="kw">per </span></a><a class="txt" onclick="hs(this)" href="javascript:()"><span class="kw">cases </span></a><span class="hide"><a NAME="E1:54_1"/>
( <font color="Maroon" title="c1">n</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="card_1.html#NK1" title="CARD_1:NK.1">0</a>  or <font color="Maroon" title="c1">n</font> <a href="xxreal_0.html#NR4" title="XXREAL_0:NR.4">&gt;</a>  <a href="card_1.html#NK1" title="CARD_1:NK.1">0</a>  )
 </span>;<br/><div class="add"><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="54_1_1"><span class="kw">suppose </span></a><a NAME="E1:54_1_1"/><span class="lab"><font color="Green" title="E38">A1</font></span>: 
<font color="Maroon" title="c1">n</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="card_1.html#NK1" title="CARD_1:NK.1">0</a> 
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide">  ex <font color="Olive" title="b1">J</font> being  <a href="relat_1.html#V2" title="RELAT_1:attr.2">non-empty</a>  <a href="matrixj2.html#NM1" title="MATRIXJ2:NM.1">FinSequence_of_Jordan_block</a> of <font color="Maroon" title="c2">K</font> ex <font color="Olive" title="b2">P</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 <br/>(  <a href="wsierp_1.html#K3" title="WSIERP_1:func.3">Sum</a> <span class="p1">(<span class="default"><a href="matrixj1.html#K10" title="MATRIXJ1:func.10">Len</a> <font color="Olive" title="b1">J</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c1">n</font> &amp; <font color="Olive" title="b2">P</font> is  <a href="matrix_6.html#V1" title="MATRIX_6:attr.1">invertible</a>  &amp; <font color="Maroon" title="c3">M</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><font color="Olive" title="b2">P</font> <a href="matrix_3.html#K4" title="MATRIX_3:func.4">*</a> <span class="p2">(<span class="default"><a href="matrixj1.html#K20" title="MATRIXJ1:func.20">block_diagonal</a> <font color="Olive" title="b1">J</font>,<span class="p3">(<span class="default"><a href="struct_0.html#K4" title="STRUCT_0:func.4">0.</a> <font color="Maroon" title="c2">K</font></span>)</span></span>)</span></span>)</span> <a href="matrix_3.html#K4" title="MATRIX_3:func.4">*</a> <span class="p1">(<span class="default"><font color="Olive" title="b2">P</font> <a href="matrix_6.html#K5" title="MATRIX_6:func.5">~</a> </span>)</span> )</span><br/><div class="add"><span class="kw">then </span><span class="kw">reconsider </span><font color="Maroon" title="c4">P</font> =  <a href="xboole_0.html#K1" title="XBOOLE_0:func.1">{}</a>  as   <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> <span class="kw">by</span> <span class="lab"><a class="ref" href="matrix_1.html#T13" title="MATRIX_1:th.13">MATRIX_1:13</a></span>;<br/><span class="kw">reconsider </span><font color="Maroon" title="c5">J</font> =  <a href="xboole_0.html#K1" title="XBOOLE_0:func.1">{}</a>  as   <a href="matrixj2.html#NM1" title="MATRIXJ2:NM.1">FinSequence_of_Jordan_block</a> of <font color="Maroon" title="c2">K</font> <span class="kw">by</span> <span class="lab"><a class="txt" href="matrixj2.html#E13"><span class="lab"><font color="Green" title="E12">Lm2</font></span></a></span>;<br/><span class="kw">reconsider </span><font color="Maroon" title="c6">J</font> = <font color="Maroon" title="c5">J</font> as   <a href="relat_1.html#V2" title="RELAT_1:attr.2">non-empty</a>  <a href="matrixj2.html#NM1" title="MATRIXJ2:NM.1">FinSequence_of_Jordan_block</a> of <font color="Maroon" title="c2">K</font> ;<br/><span class="kw">take </span>
<font color="Maroon" title="c6">J</font>
; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide">  ex <font color="Olive" title="b1">P</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 <br/>(  <a href="wsierp_1.html#K3" title="WSIERP_1:func.3">Sum</a> <span class="p1">(<span class="default"><a href="matrixj1.html#K10" title="MATRIXJ1:func.10">Len</a> <font color="Maroon" title="c6">J</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c1">n</font> &amp; <font color="Olive" title="b1">P</font> is  <a href="matrix_6.html#V1" title="MATRIX_6:attr.1">invertible</a>  &amp; <font color="Maroon" title="c3">M</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><font color="Olive" title="b1">P</font> <a href="matrix_3.html#K4" title="MATRIX_3:func.4">*</a> <span class="p2">(<span class="default"><a href="matrixj1.html#K20" title="MATRIXJ1:func.20">block_diagonal</a> <font color="Maroon" title="c6">J</font>,<span class="p3">(<span class="default"><a href="struct_0.html#K4" title="STRUCT_0:func.4">0.</a> <font color="Maroon" title="c2">K</font></span>)</span></span>)</span></span>)</span> <a href="matrix_3.html#K4" title="MATRIX_3:func.4">*</a> <span class="p1">(<span class="default"><font color="Olive" title="b1">P</font> <a href="matrix_6.html#K5" title="MATRIX_6:func.5">~</a> </span>)</span> )</span><br/><span class="kw">take </span>
<font color="Maroon" title="c4">P</font>
; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> (  <a href="wsierp_1.html#K3" title="WSIERP_1:func.3">Sum</a> <span class="p1">(<span class="default"><a href="matrixj1.html#K10" title="MATRIXJ1:func.10">Len</a> <font color="Maroon" title="c6">J</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c1">n</font> &amp; <font color="Maroon" title="c4">P</font> is  <a href="matrix_6.html#V1" title="MATRIX_6:attr.1">invertible</a>  &amp; <font color="Maroon" title="c3">M</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><font color="Maroon" title="c4">P</font> <a href="matrix_3.html#K4" title="MATRIX_3:func.4">*</a> <span class="p2">(<span class="default"><a href="matrixj1.html#K20" title="MATRIXJ1:func.20">block_diagonal</a> <font color="Maroon" title="c6">J</font>,<span class="p3">(<span class="default"><a href="struct_0.html#K4" title="STRUCT_0:func.4">0.</a> <font color="Maroon" title="c2">K</font></span>)</span></span>)</span></span>)</span> <a href="matrix_3.html#K4" title="MATRIX_3:func.4">*</a> <span class="p1">(<span class="default"><font color="Maroon" title="c4">P</font> <a href="matrix_6.html#K5" title="MATRIX_6:func.5">~</a> </span>)</span> )</span><br/><span class="lab"><font color="Green" title="E39">A2</font></span>:  <a href="matrixj1.html#K10" title="MATRIXJ1:func.10">Len</a> <font color="Maroon" title="c6">J</font> = 
 <a href="finseq_1.html#K6" title="FINSEQ_1:func.6">&lt;*&gt;</a> <a href="numbers.html#K5" title="NUMBERS:func.5">NAT</a> 
<span class="kw">by</span> <span class="lab"><a class="ref" href="card_1.html#T47" title="CARD_1:th.47">CARD_1:47</a></span>
<br/>.= 
 <a href="finseq_1.html#K6" title="FINSEQ_1:func.6">&lt;*&gt;</a> <a href="numbers.html#K1" title="NUMBERS:func.1">REAL</a> 

;<br/><span class="kw">hence </span><a NAME="E6:54_1_1"/>
 <a href="wsierp_1.html#K3" title="WSIERP_1:func.3">Sum</a> <span class="p1">(<span class="default"><a href="matrixj1.html#K10" title="MATRIXJ1:func.10">Len</a> <font color="Maroon" title="c6">J</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c1">n</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:54_1_1"><span class="lab"><font color="Green" title="E38">A1</font></span></a>, <a class="ref" href="rvsum_1.html#T102" title="RVSUM_1:th.102">RVSUM_1:102</a></span>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> ( <font color="Maroon" title="c4">P</font> is  <a href="matrix_6.html#V1" title="MATRIX_6:attr.1">invertible</a>  &amp; <font color="Maroon" title="c3">M</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><font color="Maroon" title="c4">P</font> <a href="matrix_3.html#K4" title="MATRIX_3:func.4">*</a> <span class="p2">(<span class="default"><a href="matrixj1.html#K20" title="MATRIXJ1:func.20">block_diagonal</a> <font color="Maroon" title="c6">J</font>,<span class="p3">(<span class="default"><a href="struct_0.html#K4" title="STRUCT_0:func.4">0.</a> <font color="Maroon" title="c2">K</font></span>)</span></span>)</span></span>)</span> <a href="matrix_3.html#K4" title="MATRIX_3:func.4">*</a> <span class="p1">(<span class="default"><font color="Maroon" title="c4">P</font> <a href="matrix_6.html#K5" title="MATRIX_6:func.5">~</a> </span>)</span> )</span><br/><a NAME="E7:54_1_1"/><span class="lab"><font color="Green" title="E40">A3</font></span>: 
 <a href="group_1.html#K1" title="GROUP_1:func.1">1_</a> <font color="Maroon" title="c2">K</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">K</font>
 ;<br/><a NAME="E8:54_1_1"/>
 <a href="matrix_3.html#K12" title="MATRIX_3:func.12">Det</a> <font color="Maroon" title="c4">P</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="group_1.html#K1" title="GROUP_1:func.1">1_</a> <font color="Maroon" title="c2">K</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:54_1_1"><span class="lab"><font color="Green" title="E38">A1</font></span></a>, <a class="ref" href="matrixr2.html#T41" title="MATRIXR2:th.41">MATRIXR2:41</a></span>;<br/><span class="kw">hence </span><a NAME="E9:54_1_1"/>
<font color="Maroon" title="c4">P</font> is  <a href="matrix_6.html#V1" title="MATRIX_6:attr.1">invertible</a> 
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E7:54_1_1"><span class="lab"><font color="Green" title="E40">A3</font></span></a>, <a class="ref" href="laplace.html#T34" title="LAPLACE:th.34">LAPLACE:34</a></span>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> <font color="Maroon" title="c3">M</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><font color="Maroon" title="c4">P</font> <a href="matrix_3.html#K4" title="MATRIX_3:func.4">*</a> <span class="p2">(<span class="default"><a href="matrixj1.html#K20" title="MATRIXJ1:func.20">block_diagonal</a> <font color="Maroon" title="c6">J</font>,<span class="p3">(<span class="default"><a href="struct_0.html#K4" title="STRUCT_0:func.4">0.</a> <font color="Maroon" title="c2">K</font></span>)</span></span>)</span></span>)</span> <a href="matrix_3.html#K4" title="MATRIX_3:func.4">*</a> <span class="p1">(<span class="default"><font color="Maroon" title="c4">P</font> <a href="matrix_6.html#K5" title="MATRIX_6:func.5">~</a> </span>)</span></span><br/><span class="kw">reconsider </span><font color="Maroon" title="c7">B</font> =  <a href="matrixj1.html#K20" title="MATRIXJ1:func.20">block_diagonal</a> <font color="Maroon" title="c6">J</font>,<span class="p1">(<span class="default"><a href="struct_0.html#K4" title="STRUCT_0:func.4">0.</a> <font color="Maroon" title="c2">K</font></span>)</span> as   <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> <span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:54_1_1"><span class="lab"><font color="Green" title="E38">A1</font></span></a>, <a class="txt" href="#E5:54_1_1"><span class="lab"><font color="Green" title="E39">A2</font></span></a>, <a class="ref" href="rvsum_1.html#T102" title="RVSUM_1:th.102">RVSUM_1:102</a></span>;<br/><a NAME="E11:54_1_1"/>
<font color="Maroon" title="c3">M</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><font color="Maroon" title="c4">P</font> <a href="matrix_6.html#K4" title="MATRIX_6:func.4">*</a> <font color="Maroon" title="c7">B</font></span>)</span> <a href="matrix_6.html#K4" title="MATRIX_6:func.4">*</a> <span class="p1">(<span class="default"><font color="Maroon" title="c4">P</font> <a href="matrix_6.html#K5" title="MATRIX_6:func.5">~</a> </span>)</span>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:54_1_1"><span class="lab"><font color="Green" title="E38">A1</font></span></a>, <a class="ref" href="matrix_1.html#T36" title="MATRIX_1:th.36">MATRIX_1:36</a></span>;<br/><span class="kw">hence </span><a NAME="E12:54_1_1"/>
<font color="Maroon" title="c3">M</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><font color="Maroon" title="c4">P</font> <a href="matrix_3.html#K4" title="MATRIX_3:func.4">*</a> <span class="p2">(<span class="default"><a href="matrixj1.html#K20" title="MATRIXJ1:func.20">block_diagonal</a> <font color="Maroon" title="c6">J</font>,<span class="p3">(<span class="default"><a href="struct_0.html#K4" title="STRUCT_0:func.4">0.</a> <font color="Maroon" title="c2">K</font></span>)</span></span>)</span></span>)</span> <a href="matrix_3.html#K4" title="MATRIX_3:func.4">*</a> <span class="p1">(<span class="default"><font color="Maroon" title="c4">P</font> <a href="matrix_6.html#K5" title="MATRIX_6:func.5">~</a> </span>)</span>
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> verum</span><br/></div><span class="kw">end;</span></div><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="54_1_2"><span class="kw">suppose </span></a><a NAME="E1:54_1_2"/><span class="lab"><font color="Green" title="E38">A4</font></span>: 
<font color="Maroon" title="c1">n</font> <a href="xxreal_0.html#NR4" title="XXREAL_0:NR.4">&gt;</a>  <a href="card_1.html#NK1" title="CARD_1:NK.1">0</a> 
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide">  ex <font color="Olive" title="b1">J</font> being  <a href="relat_1.html#V2" title="RELAT_1:attr.2">non-empty</a>  <a href="matrixj2.html#NM1" title="MATRIXJ2:NM.1">FinSequence_of_Jordan_block</a> of <font color="Maroon" title="c2">K</font> ex <font color="Olive" title="b2">P</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 <br/>(  <a href="wsierp_1.html#K3" title="WSIERP_1:func.3">Sum</a> <span class="p1">(<span class="default"><a href="matrixj1.html#K10" title="MATRIXJ1:func.10">Len</a> <font color="Olive" title="b1">J</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c1">n</font> &amp; <font color="Olive" title="b2">P</font> is  <a href="matrix_6.html#V1" title="MATRIX_6:attr.1">invertible</a>  &amp; <font color="Maroon" title="c3">M</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><font color="Olive" title="b2">P</font> <a href="matrix_3.html#K4" title="MATRIX_3:func.4">*</a> <span class="p2">(<span class="default"><a href="matrixj1.html#K20" title="MATRIXJ1:func.20">block_diagonal</a> <font color="Olive" title="b1">J</font>,<span class="p3">(<span class="default"><a href="struct_0.html#K4" title="STRUCT_0:func.4">0.</a> <font color="Maroon" title="c2">K</font></span>)</span></span>)</span></span>)</span> <a href="matrix_3.html#K4" title="MATRIX_3:func.4">*</a> <span class="p1">(<span class="default"><font color="Olive" title="b2">P</font> <a href="matrix_6.html#K5" title="MATRIX_6:func.5">~</a> </span>)</span> )</span><br/><div class="add"><span class="kw">set </span><font color="Maroon" title="c4">V</font> = <font color="Maroon" title="c1">n</font> <a href="matrix13.html#K13" title="MATRIX13:func.13">-VectSp_over</a> <font color="Maroon" title="c2">K</font>;<br/><span class="kw">consider </span><font color="Maroon" title="c5">B</font> being    <a href="matrlin.html#M1" title="MATRLIN:mode.1">OrdBasis</a> of <font color="Maroon" title="c1">n</font> <a href="matrix13.html#K13" title="MATRIX13:func.13">-VectSp_over</a> <font color="Maroon" title="c2">K</font>;<br/><span class="lab"><font color="Green" title="E39">A5</font></span>:  <a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <font color="Maroon" title="c5">B</font> = 
 <a href="vectsp_9.html#K1" title="VECTSP_9:func.1">dim</a> <span class="p1">(<span class="default"><font color="Maroon" title="c1">n</font> <a href="matrix13.html#K13" title="MATRIX13:func.13">-VectSp_over</a> <font color="Maroon" title="c2">K</font></span>)</span>
<span class="kw">by</span> <span class="lab"><a class="ref" href="matrlin2.html#T21" title="MATRLIN2:th.21">MATRLIN2:21</a></span>
<br/>.= 
<font color="Maroon" title="c1">n</font>
<span class="kw">by</span> <span class="lab"><a class="ref" href="matrix13.html#T112" title="MATRIX13:th.112">MATRIX13:112</a></span>
;<br/><span class="kw">then </span><span class="kw">reconsider </span><font color="Maroon" title="c6">M9</font> = <font color="Maroon" title="c3">M</font> as   <a href="matrix_1.html#NM5" title="MATRIX_1:NM.5">Matrix</a> of  <a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <font color="Maroon" title="c5">B</font>,<font color="Maroon" title="c2">K</font> ;<br/><span class="kw">set </span><font color="Maroon" title="c7">T</font> =  <a href="matrlin2.html#K5" title="MATRLIN2:func.5">Mx2Tran</a> <font color="Maroon" title="c6">M9</font>,<font color="Maroon" title="c5">B</font>,<font color="Maroon" title="c5">B</font>;<br/><a NAME="E5:54_1_2"/>
 <a href="vectsp_9.html#K1" title="VECTSP_9:func.1">dim</a> <span class="p1">(<span class="default"><font color="Maroon" title="c1">n</font> <a href="matrix13.html#K13" title="MATRIX13:func.13">-VectSp_over</a> <font color="Maroon" title="c2">K</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c1">n</font>
 <span class="kw">by</span> <span class="lab"><a class="ref" href="matrix13.html#T112" title="MATRIX13:th.112">MATRIX13:112</a></span>;<br/><a NAME="E6:54_1_2"/><span class="kw">then </span>
not <font color="Maroon" title="c1">n</font> <a href="matrix13.html#K13" title="MATRIX13:func.13">-VectSp_over</a> <font color="Maroon" title="c2">K</font> is  <a href="struct_0.html#V7" title="STRUCT_0:attr.7">trivial</a> 
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:54_1_2"><span class="lab"><font color="Green" title="E38">A4</font></span></a>, <a class="ref" href="matrlin2.html#T42" title="MATRLIN2:th.42">MATRLIN2:42</a></span>;<br/><span class="kw">then </span><span class="kw">consider </span><font color="Maroon" title="c8">J</font> being   <a href="relat_1.html#V2" title="RELAT_1:attr.2">non-empty</a>  <a href="matrixj2.html#NM1" title="MATRIXJ2:NM.1">FinSequence_of_Jordan_block</a> of <font color="Maroon" title="c2">K</font>, <font color="Maroon" title="c9">b1</font> being    <a href="matrlin.html#M1" title="MATRLIN:mode.1">OrdBasis</a> of <font color="Maroon" title="c1">n</font> <a href="matrix13.html#K13" title="MATRIX13:func.13">-VectSp_over</a> <font color="Maroon" title="c2">K</font><span class="kw"> such that </span><br/><a NAME="E8:54_1_2"/><span class="lab"><font color="Green" title="E40">A6</font></span>: 
 <a href="matrlin2.html#K1" title="MATRLIN2:func.1">AutMt</a> <span class="p1">(<span class="default"><a href="matrlin2.html#K5" title="MATRLIN2:func.5">Mx2Tran</a> <font color="Maroon" title="c6">M9</font>,<font color="Maroon" title="c5">B</font>,<font color="Maroon" title="c5">B</font></span>)</span>,<font color="Maroon" title="c9">b1</font>,<font color="Maroon" title="c9">b1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="matrixj1.html#K20" title="MATRIXJ1:func.20">block_diagonal</a> <font color="Maroon" title="c8">J</font>,<span class="p1">(<span class="default"><a href="struct_0.html#K4" title="STRUCT_0:func.4">0.</a> <font color="Maroon" title="c2">K</font></span>)</span>
 <span class="kw">and </span><br/><a NAME="E9:54_1_2"/>
for <font color="Olive" title="b1">L</font> being  <a href="vectsp_1.html#NM4" title="VECTSP_1:NM.4">Scalar</a> of <font color="Maroon" title="c2">K</font> holds <br/> ( <font color="Olive" title="b1">L</font> is    <a href="vectsp11.html#M1" title="VECTSP11:mode.1">eigenvalue</a> of  <a href="matrlin2.html#K5" title="MATRLIN2:func.5">Mx2Tran</a> <font color="Maroon" title="c6">M9</font>,<font color="Maroon" title="c5">B</font>,<font color="Maroon" title="c5">B</font> iff  ex <font color="Olive" title="b2">i</font> being  <a href="nat_1.html#NM1" title="NAT_1:NM.1">Nat</a> st <br/>( <font color="Olive" title="b2">i</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="finseq_1.html#K4" title="FINSEQ_1:func.4">dom</a> <font color="Maroon" title="c8">J</font> &amp; <font color="Maroon" title="c8">J</font> <a href="matrixj1.html#K14" title="MATRIXJ1:func.14">.</a> <font color="Olive" title="b2">i</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="matrixj2.html#K2" title="MATRIXJ2:func.2">Jordan_block</a> <font color="Olive" title="b1">L</font>,<span class="p1">(<span class="default"><a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <span class="p2">(<span class="default"><font color="Maroon" title="c8">J</font> <a href="matrixj1.html#K14" title="MATRIXJ1:func.14">.</a> <font color="Olive" title="b2">i</font></span>)</span></span>)</span> ) )
 <span class="kw">by</span> <span class="lab"><a class="ref" href="matrixj2.html#T31" target="_self" title="MATRIXJ2:th.31">Th31</a></span>;<br/><a NAME="E10:54_1_2"/><span class="lab"><font color="Green" title="E41">A7</font></span>: 
 <a href="relat_1.html#NK2" title="RELAT_1:NK.2">dom</a> <span class="p1">(<span class="default"><a href="matrlin2.html#K5" title="MATRLIN2:func.5">Mx2Tran</a> <font color="Maroon" title="c6">M9</font>,<font color="Maroon" title="c5">B</font>,<font color="Maroon" title="c5">B</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="struct_0.html#K2" title="STRUCT_0:func.2">[#]</a> <span class="p1">(<span class="default"><font color="Maroon" title="c1">n</font> <a href="matrix13.html#K13" title="MATRIX13:func.13">-VectSp_over</a> <font color="Maroon" title="c2">K</font></span>)</span>
 <span class="kw">by</span> <span class="lab"><a class="ref" href="funct_2.html#D1" title="FUNCT_2:def.1">FUNCT_2:def 1</a></span>;<br/><span class="kw">reconsider </span><font color="Maroon" title="c10">P</font> =  <a href="matrlin2.html#K3" title="MATRLIN2:func.3">AutEqMt</a> <span class="p1">(<span class="default"><a href="matrlin2.html#K7" title="MATRLIN2:func.7">id</a> <span class="p2">(<span class="default"><font color="Maroon" title="c1">n</font> <a href="matrix13.html#K13" title="MATRIX13:func.13">-VectSp_over</a> <font color="Maroon" title="c2">K</font></span>)</span></span>)</span>,<font color="Maroon" title="c5">B</font>,<font color="Maroon" title="c9">b1</font> as   <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> <span class="kw">by</span> <span class="lab"><a class="txt" href="#E3:54_1_2"><span class="lab"><font color="Green" title="E39">A5</font></span></a></span>;<br/><span class="kw">take </span>
<font color="Maroon" title="c8">J</font>
; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide">  ex <font color="Olive" title="b1">P</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 <br/>(  <a href="wsierp_1.html#K3" title="WSIERP_1:func.3">Sum</a> <span class="p1">(<span class="default"><a href="matrixj1.html#K10" title="MATRIXJ1:func.10">Len</a> <font color="Maroon" title="c8">J</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c1">n</font> &amp; <font color="Olive" title="b1">P</font> is  <a href="matrix_6.html#V1" title="MATRIX_6:attr.1">invertible</a>  &amp; <font color="Maroon" title="c3">M</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><font color="Olive" title="b1">P</font> <a href="matrix_3.html#K4" title="MATRIX_3:func.4">*</a> <span class="p2">(<span class="default"><a href="matrixj1.html#K20" title="MATRIXJ1:func.20">block_diagonal</a> <font color="Maroon" title="c8">J</font>,<span class="p3">(<span class="default"><a href="struct_0.html#K4" title="STRUCT_0:func.4">0.</a> <font color="Maroon" title="c2">K</font></span>)</span></span>)</span></span>)</span> <a href="matrix_3.html#K4" title="MATRIX_3:func.4">*</a> <span class="p1">(<span class="default"><font color="Olive" title="b1">P</font> <a href="matrix_6.html#K5" title="MATRIX_6:func.5">~</a> </span>)</span> )</span><br/><span class="kw">take </span>
<font color="Maroon" title="c10">P</font>
; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> (  <a href="wsierp_1.html#K3" title="WSIERP_1:func.3">Sum</a> <span class="p1">(<span class="default"><a href="matrixj1.html#K10" title="MATRIXJ1:func.10">Len</a> <font color="Maroon" title="c8">J</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c1">n</font> &amp; <font color="Maroon" title="c10">P</font> is  <a href="matrix_6.html#V1" title="MATRIX_6:attr.1">invertible</a>  &amp; <font color="Maroon" title="c3">M</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><font color="Maroon" title="c10">P</font> <a href="matrix_3.html#K4" title="MATRIX_3:func.4">*</a> <span class="p2">(<span class="default"><a href="matrixj1.html#K20" title="MATRIXJ1:func.20">block_diagonal</a> <font color="Maroon" title="c8">J</font>,<span class="p3">(<span class="default"><a href="struct_0.html#K4" title="STRUCT_0:func.4">0.</a> <font color="Maroon" title="c2">K</font></span>)</span></span>)</span></span>)</span> <a href="matrix_3.html#K4" title="MATRIX_3:func.4">*</a> <span class="p1">(<span class="default"><font color="Maroon" title="c10">P</font> <a href="matrix_6.html#K5" title="MATRIX_6:func.5">~</a> </span>)</span> )</span><br/><a NAME="E12:54_1_2"/><span class="lab"><font color="Green" title="E42">A8</font></span>: 
(  <a href="matrix_1.html#K1" title="MATRIX_1:func.1">width</a> <font color="Maroon" title="c10">P</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c1">n</font> &amp;  <a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <span class="p1">(<span class="default"><font color="Maroon" title="c10">P</font> <a href="matrix_6.html#K5" title="MATRIX_6:func.5">~</a> </span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c1">n</font> )
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:54_1_2"><span class="lab"><font color="Green" title="E38">A4</font></span></a>, <a class="ref" href="matrix_1.html#T24" title="MATRIX_1:th.24">MATRIX_1:24</a></span>;<br/><a NAME="E13:54_1_2"/><span class="lab"><font color="Green" title="E43">A9</font></span>: 
 <a href="relat_1.html#K2" title="RELAT_1:func.2">rng</a> <span class="p1">(<span class="default"><a href="matrlin2.html#K5" title="MATRLIN2:func.5">Mx2Tran</a> <font color="Maroon" title="c6">M9</font>,<font color="Maroon" title="c5">B</font>,<font color="Maroon" title="c5">B</font></span>)</span> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a>  <a href="struct_0.html#K2" title="STRUCT_0:func.2">[#]</a> <span class="p1">(<span class="default"><font color="Maroon" title="c1">n</font> <a href="matrix13.html#K13" title="MATRIX13:func.13">-VectSp_over</a> <font color="Maroon" title="c2">K</font></span>)</span>
 <span class="kw">by</span> <span class="lab"><a class="ref" href="relat_1.html#D19" title="RELAT_1:def.19">RELAT_1:def 19</a></span>;<br/><span class="lab"><font color="Green" title="E44">A10</font></span>:  <a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <font color="Maroon" title="c9">b1</font> = 
 <a href="vectsp_9.html#K1" title="VECTSP_9:func.1">dim</a> <span class="p1">(<span class="default"><font color="Maroon" title="c1">n</font> <a href="matrix13.html#K13" title="MATRIX13:func.13">-VectSp_over</a> <font color="Maroon" title="c2">K</font></span>)</span>
<span class="kw">by</span> <span class="lab"><a class="ref" href="matrlin2.html#T21" title="MATRLIN2:th.21">MATRLIN2:21</a></span>
<br/>.= 
<font color="Maroon" title="c1">n</font>
<span class="kw">by</span> <span class="lab"><a class="ref" href="matrix13.html#T112" title="MATRIX13:th.112">MATRIX13:112</a></span>
;<br/><a NAME="E15:54_1_2"/><span class="kw">then </span><span class="lab"><font color="Green" title="E45">A11</font></span>: 
(  <a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <span class="p1">(<span class="default"><a href="matrlin2.html#K1" title="MATRLIN2:func.1">AutMt</a> <span class="p2">(<span class="default"><a href="matrlin2.html#K5" title="MATRLIN2:func.5">Mx2Tran</a> <font color="Maroon" title="c6">M9</font>,<font color="Maroon" title="c5">B</font>,<font color="Maroon" title="c5">B</font></span>)</span>,<font color="Maroon" title="c9">b1</font>,<font color="Maroon" title="c9">b1</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c1">n</font> &amp;  <a href="matrix_1.html#K1" title="MATRIX_1:func.1">width</a> <span class="p1">(<span class="default"><a href="matrlin2.html#K1" title="MATRLIN2:func.1">AutMt</a> <span class="p2">(<span class="default"><a href="matrlin2.html#K5" title="MATRLIN2:func.5">Mx2Tran</a> <font color="Maroon" title="c6">M9</font>,<font color="Maroon" title="c5">B</font>,<font color="Maroon" title="c5">B</font></span>)</span>,<font color="Maroon" title="c9">b1</font>,<font color="Maroon" title="c9">b1</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c1">n</font> )
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:54_1_2"><span class="lab"><font color="Green" title="E38">A4</font></span></a>, <a class="ref" href="matrix_1.html#T24" title="MATRIX_1:th.24">MATRIX_1:24</a></span>;<br/><span class="kw">thus </span> <a href="wsierp_1.html#K3" title="WSIERP_1:func.3">Sum</a> <span class="p1">(<span class="default"><a href="matrixj1.html#K10" title="MATRIXJ1:func.10">Len</a> <font color="Maroon" title="c8">J</font></span>)</span> = 
 <a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <span class="p1">(<span class="default"><a href="matrlin2.html#K1" title="MATRLIN2:func.1">AutMt</a> <span class="p2">(<span class="default"><a href="matrlin2.html#K5" title="MATRLIN2:func.5">Mx2Tran</a> <font color="Maroon" title="c6">M9</font>,<font color="Maroon" title="c5">B</font>,<font color="Maroon" title="c5">B</font></span>)</span>,<font color="Maroon" title="c9">b1</font>,<font color="Maroon" title="c9">b1</font></span>)</span>
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E8:54_1_2"><span class="lab"><font color="Green" title="E40">A6</font></span></a>, <a class="ref" href="matrixj1.html#D5" title="MATRIXJ1:def.5">MATRIXJ1:def 5</a></span>
<br/>.= 
<font color="Maroon" title="c1">n</font>
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E14:54_1_2"><span class="lab"><font color="Green" title="E44">A10</font></span></a>, <a class="ref" href="matrix_1.html#D3" title="MATRIX_1:def.3">MATRIX_1:def 3</a></span>
; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> ( <font color="Maroon" title="c10">P</font> is  <a href="matrix_6.html#V1" title="MATRIX_6:attr.1">invertible</a>  &amp; <font color="Maroon" title="c3">M</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><font color="Maroon" title="c10">P</font> <a href="matrix_3.html#K4" title="MATRIX_3:func.4">*</a> <span class="p2">(<span class="default"><a href="matrixj1.html#K20" title="MATRIXJ1:func.20">block_diagonal</a> <font color="Maroon" title="c8">J</font>,<span class="p3">(<span class="default"><a href="struct_0.html#K4" title="STRUCT_0:func.4">0.</a> <font color="Maroon" title="c2">K</font></span>)</span></span>)</span></span>)</span> <a href="matrix_3.html#K4" title="MATRIX_3:func.4">*</a> <span class="p1">(<span class="default"><font color="Maroon" title="c10">P</font> <a href="matrix_6.html#K5" title="MATRIX_6:func.5">~</a> </span>)</span> )</span><br/><span class="kw">thus </span><a NAME="E17:54_1_2"/>
<font color="Maroon" title="c10">P</font> is  <a href="matrix_6.html#V1" title="MATRIX_6:attr.1">invertible</a> 
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E3:54_1_2"><span class="lab"><font color="Green" title="E39">A5</font></span></a>, <a class="ref" href="matrlin2.html#T29" title="MATRLIN2:th.29">MATRLIN2:29</a></span>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> <font color="Maroon" title="c3">M</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><font color="Maroon" title="c10">P</font> <a href="matrix_3.html#K4" title="MATRIX_3:func.4">*</a> <span class="p2">(<span class="default"><a href="matrixj1.html#K20" title="MATRIXJ1:func.20">block_diagonal</a> <font color="Maroon" title="c8">J</font>,<span class="p3">(<span class="default"><a href="struct_0.html#K4" title="STRUCT_0:func.4">0.</a> <font color="Maroon" title="c2">K</font></span>)</span></span>)</span></span>)</span> <a href="matrix_3.html#K4" title="MATRIX_3:func.4">*</a> <span class="p1">(<span class="default"><font color="Maroon" title="c10">P</font> <a href="matrix_6.html#K5" title="MATRIX_6:func.5">~</a> </span>)</span></span><br/><span class="kw">thus </span><font color="Maroon" title="c3">M</font> = 
 <a href="matrlin2.html#K1" title="MATRLIN2:func.1">AutMt</a> <span class="p1">(<span class="default"><a href="matrlin2.html#K5" title="MATRLIN2:func.5">Mx2Tran</a> <font color="Maroon" title="c6">M9</font>,<font color="Maroon" title="c5">B</font>,<font color="Maroon" title="c5">B</font></span>)</span>,<font color="Maroon" title="c5">B</font>,<font color="Maroon" title="c5">B</font>
<span class="kw">by</span> <span class="lab"><a class="ref" href="matrlin2.html#T36" title="MATRLIN2:th.36">MATRLIN2:36</a></span>
<br/>.= 
 <a href="matrlin2.html#K1" title="MATRLIN2:func.1">AutMt</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="matrlin2.html#K5" title="MATRLIN2:func.5">Mx2Tran</a> <font color="Maroon" title="c6">M9</font>,<font color="Maroon" title="c5">B</font>,<font color="Maroon" title="c5">B</font></span>)</span> <a href="matrlin2.html#K10" title="MATRLIN2:func.10">*</a> <span class="p2">(<span class="default"><a href="matrlin2.html#K7" title="MATRLIN2:func.7">id</a> <span class="p3">(<span class="default"><font color="Maroon" title="c1">n</font> <a href="matrix13.html#K13" title="MATRIX13:func.13">-VectSp_over</a> <font color="Maroon" title="c2">K</font></span>)</span></span>)</span></span>)</span>,<font color="Maroon" title="c5">B</font>,<font color="Maroon" title="c5">B</font>
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E10:54_1_2"><span class="lab"><font color="Green" title="E41">A7</font></span></a>, <a class="ref" href="relat_1.html#T78" title="RELAT_1:th.78">RELAT_1:78</a></span>
<br/>.= 
<span class="p1">(<span class="default"><a href="matrlin2.html#K1" title="MATRLIN2:func.1">AutMt</a> <span class="p2">(<span class="default"><a href="matrlin2.html#K7" title="MATRLIN2:func.7">id</a> <span class="p3">(<span class="default"><font color="Maroon" title="c1">n</font> <a href="matrix13.html#K13" title="MATRIX13:func.13">-VectSp_over</a> <font color="Maroon" title="c2">K</font></span>)</span></span>)</span>,<font color="Maroon" title="c5">B</font>,<font color="Maroon" title="c9">b1</font></span>)</span> <a href="matrix_3.html#K4" title="MATRIX_3:func.4">*</a> <span class="p1">(<span class="default"><a href="matrlin2.html#K1" title="MATRLIN2:func.1">AutMt</a> <span class="p2">(<span class="default"><a href="matrlin2.html#K5" title="MATRLIN2:func.5">Mx2Tran</a> <font color="Maroon" title="c6">M9</font>,<font color="Maroon" title="c5">B</font>,<font color="Maroon" title="c5">B</font></span>)</span>,<font color="Maroon" title="c9">b1</font>,<font color="Maroon" title="c5">B</font></span>)</span>
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:54_1_2"><span class="lab"><font color="Green" title="E38">A4</font></span></a>, <a class="txt" href="#E3:54_1_2"><span class="lab"><font color="Green" title="E39">A5</font></span></a>, <a class="txt" href="#E14:54_1_2"><span class="lab"><font color="Green" title="E44">A10</font></span></a>, <a class="ref" href="matrlin.html#T46" title="MATRLIN:th.46">MATRLIN:46</a></span>
<br/>.= 
<font color="Maroon" title="c10">P</font> <a href="matrix_3.html#K4" title="MATRIX_3:func.4">*</a> <span class="p1">(<span class="default"><a href="matrlin2.html#K1" title="MATRLIN2:func.1">AutMt</a> <span class="p2">(<span class="default"><a href="matrlin2.html#K5" title="MATRLIN2:func.5">Mx2Tran</a> <font color="Maroon" title="c6">M9</font>,<font color="Maroon" title="c5">B</font>,<font color="Maroon" title="c5">B</font></span>)</span>,<font color="Maroon" title="c9">b1</font>,<font color="Maroon" title="c5">B</font></span>)</span>
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E3:54_1_2"><span class="lab"><font color="Green" title="E39">A5</font></span></a>, <a class="txt" href="#E14:54_1_2"><span class="lab"><font color="Green" title="E44">A10</font></span></a>, <a class="ref" href="matrlin2.html#D2" title="MATRLIN2:def.2">MATRLIN2:def 2</a></span>
<br/>.= 
<font color="Maroon" title="c10">P</font> <a href="matrix_3.html#K4" title="MATRIX_3:func.4">*</a> <span class="p1">(<span class="default"><a href="matrlin2.html#K1" title="MATRLIN2:func.1">AutMt</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="matrlin2.html#K7" title="MATRLIN2:func.7">id</a> <span class="p4">(<span class="default"><font color="Maroon" title="c1">n</font> <a href="matrix13.html#K13" title="MATRIX13:func.13">-VectSp_over</a> <font color="Maroon" title="c2">K</font></span>)</span></span>)</span> <a href="matrlin2.html#K10" title="MATRLIN2:func.10">*</a> <span class="p3">(<span class="default"><a href="matrlin2.html#K5" title="MATRLIN2:func.5">Mx2Tran</a> <font color="Maroon" title="c6">M9</font>,<font color="Maroon" title="c5">B</font>,<font color="Maroon" title="c5">B</font></span>)</span></span>)</span>,<font color="Maroon" title="c9">b1</font>,<font color="Maroon" title="c5">B</font></span>)</span>
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E13:54_1_2"><span class="lab"><font color="Green" title="E43">A9</font></span></a>, <a class="ref" href="relat_1.html#T79" title="RELAT_1:th.79">RELAT_1:79</a></span>
<br/>.= 
<font color="Maroon" title="c10">P</font> <a href="matrix_3.html#K4" title="MATRIX_3:func.4">*</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="matrlin2.html#K1" title="MATRLIN2:func.1">AutMt</a> <span class="p3">(<span class="default"><a href="matrlin2.html#K5" title="MATRLIN2:func.5">Mx2Tran</a> <font color="Maroon" title="c6">M9</font>,<font color="Maroon" title="c5">B</font>,<font color="Maroon" title="c5">B</font></span>)</span>,<font color="Maroon" title="c9">b1</font>,<font color="Maroon" title="c9">b1</font></span>)</span> <a href="matrix_3.html#K4" title="MATRIX_3:func.4">*</a> <span class="p2">(<span class="default"><a href="matrlin2.html#K1" title="MATRLIN2:func.1">AutMt</a> <span class="p3">(<span class="default"><a href="matrlin2.html#K7" title="MATRLIN2:func.7">id</a> <span class="p4">(<span class="default"><font color="Maroon" title="c1">n</font> <a href="matrix13.html#K13" title="MATRIX13:func.13">-VectSp_over</a> <font color="Maroon" title="c2">K</font></span>)</span></span>)</span>,<font color="Maroon" title="c9">b1</font>,<font color="Maroon" title="c5">B</font></span>)</span></span>)</span>
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:54_1_2"><span class="lab"><font color="Green" title="E38">A4</font></span></a>, <a class="txt" href="#E14:54_1_2"><span class="lab"><font color="Green" title="E44">A10</font></span></a>, <a class="ref" href="matrlin.html#T46" title="MATRLIN:th.46">MATRLIN:46</a></span>
<br/>.= 
<font color="Maroon" title="c10">P</font> <a href="matrix_3.html#K4" title="MATRIX_3:func.4">*</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="matrlin2.html#K1" title="MATRLIN2:func.1">AutMt</a> <span class="p3">(<span class="default"><a href="matrlin2.html#K5" title="MATRLIN2:func.5">Mx2Tran</a> <font color="Maroon" title="c6">M9</font>,<font color="Maroon" title="c5">B</font>,<font color="Maroon" title="c5">B</font></span>)</span>,<font color="Maroon" title="c9">b1</font>,<font color="Maroon" title="c9">b1</font></span>)</span> <a href="matrix_6.html#K4" title="MATRIX_6:func.4">*</a> <span class="p2">(<span class="default"><a href="matrlin2.html#K3" title="MATRLIN2:func.3">AutEqMt</a> <span class="p3">(<span class="default"><a href="matrlin2.html#K7" title="MATRLIN2:func.7">id</a> <span class="p4">(<span class="default"><font color="Maroon" title="c1">n</font> <a href="matrix13.html#K13" title="MATRIX13:func.13">-VectSp_over</a> <font color="Maroon" title="c2">K</font></span>)</span></span>)</span>,<font color="Maroon" title="c9">b1</font>,<font color="Maroon" title="c5">B</font></span>)</span></span>)</span>
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E3:54_1_2"><span class="lab"><font color="Green" title="E39">A5</font></span></a>, <a class="txt" href="#E14:54_1_2"><span class="lab"><font color="Green" title="E44">A10</font></span></a>, <a class="ref" href="matrlin2.html#D2" title="MATRLIN2:def.2">MATRLIN2:def 2</a></span>
<br/>.= 
<font color="Maroon" title="c10">P</font> <a href="matrix_3.html#K4" title="MATRIX_3:func.4">*</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="matrlin2.html#K1" title="MATRLIN2:func.1">AutMt</a> <span class="p3">(<span class="default"><a href="matrlin2.html#K5" title="MATRLIN2:func.5">Mx2Tran</a> <font color="Maroon" title="c6">M9</font>,<font color="Maroon" title="c5">B</font>,<font color="Maroon" title="c5">B</font></span>)</span>,<font color="Maroon" title="c9">b1</font>,<font color="Maroon" title="c9">b1</font></span>)</span> <a href="matrix_3.html#K4" title="MATRIX_3:func.4">*</a> <span class="p2">(<span class="default"><font color="Maroon" title="c10">P</font> <a href="matrix_6.html#K5" title="MATRIX_6:func.5">~</a> </span>)</span></span>)</span>
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E3:54_1_2"><span class="lab"><font color="Green" title="E39">A5</font></span></a>, <a class="ref" href="matrlin2.html#T29" title="MATRLIN2:th.29">MATRLIN2:29</a></span>
<br/>.= 
<span class="p1">(<span class="default"><font color="Maroon" title="c10">P</font> <a href="matrix_3.html#K4" title="MATRIX_3:func.4">*</a> <span class="p2">(<span class="default"><a href="matrixj1.html#K20" title="MATRIXJ1:func.20">block_diagonal</a> <font color="Maroon" title="c8">J</font>,<span class="p3">(<span class="default"><a href="struct_0.html#K4" title="STRUCT_0:func.4">0.</a> <font color="Maroon" title="c2">K</font></span>)</span></span>)</span></span>)</span> <a href="matrix_3.html#K4" title="MATRIX_3:func.4">*</a> <span class="p1">(<span class="default"><font color="Maroon" title="c10">P</font> <a href="matrix_6.html#K5" title="MATRIX_6:func.5">~</a> </span>)</span>
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E8:54_1_2"><span class="lab"><font color="Green" title="E40">A6</font></span></a>, <a class="txt" href="#E12:54_1_2"><span class="lab"><font color="Green" title="E42">A8</font></span></a>, <a class="txt" href="#E15:54_1_2"><span class="lab"><font color="Green" title="E45">A11</font></span></a>, <a class="ref" href="matrix_3.html#T35" title="MATRIX_3:th.35">MATRIX_3:35</a></span>
; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> verum</span><br/></div><span class="kw">end;</span></div></div><span class="kw">end;</span></div>

</div>
