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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="vectsp_1.html#NM3" title="VECTSP_1:NM.3">Field</a> holds <br/> (  <a href="matrix_1.html#K11" title="MATRIX_1:func.11">0.</a> <font color="Olive" title="b1">K</font>,<font color="Maroon" title="c1">n</font> is  <a href="matrix_8.html#V1" title="MATRIX_8:attr.1">Idempotent</a>  &amp;  <a href="matrix_1.html#K11" title="MATRIX_1:func.11">0.</a> <font color="Olive" title="b1">K</font>,<font color="Maroon" title="c1">n</font> is  <a href="matrix_8.html#V2" title="MATRIX_8:attr.2">Nilpotent</a>  )</span><br/><span class="kw">let </span><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:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> (  <a href="matrix_1.html#K11" title="MATRIX_1:func.11">0.</a> <font color="Maroon" title="c2">K</font>,<font color="Maroon" title="c1">n</font> is  <a href="matrix_8.html#V1" title="MATRIX_8:attr.1">Idempotent</a>  &amp;  <a href="matrix_1.html#K11" title="MATRIX_1:func.11">0.</a> <font color="Maroon" title="c2">K</font>,<font color="Maroon" title="c1">n</font> is  <a href="matrix_8.html#V2" title="MATRIX_8:attr.2">Nilpotent</a>  )</span><br/>



<a NAME="E1:3"/>
(  <a href="matrix_1.html#K1" title="MATRIX_1:func.1">width</a> <span class="p1">(<span class="default"><a href="matrix_3.html#K1" title="MATRIX_3:func.1">0.</a> <font color="Maroon" title="c2">K</font>,<font color="Maroon" title="c1">n</font>,<font color="Maroon" title="c1">n</font></span>)</span> <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"><a href="matrix_3.html#K1" title="MATRIX_3:func.1">0.</a> <font color="Maroon" title="c2">K</font>,<font color="Maroon" title="c1">n</font>,<font color="Maroon" title="c1">n</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="matrix_1.html#T25" title="MATRIX_1:th.25">MATRIX_1:25</a></span>;<br/>
<a NAME="E2:3"/><span class="kw">then </span>
<span class="p1">(<span class="default"><a href="matrix_3.html#K1" title="MATRIX_3:func.1">0.</a> <font color="Maroon" title="c2">K</font>,<font color="Maroon" title="c1">n</font>,<font color="Maroon" title="c1">n</font></span>)</span> <a href="matrix_6.html#K4" title="MATRIX_6:func.4">*</a> <span class="p1">(<span class="default"><a href="matrix_1.html#K11" title="MATRIX_1:func.11">0.</a> <font color="Maroon" title="c2">K</font>,<font color="Maroon" title="c1">n</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="matrix_3.html#K1" title="MATRIX_3:func.1">0.</a> <font color="Maroon" title="c2">K</font>,<font color="Maroon" title="c1">n</font>,<font color="Maroon" title="c1">n</font>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="matrix_6.html#T1" title="MATRIX_6:th.1">MATRIX_6:1</a></span>;<br/>
<span class="kw">hence </span><a NAME="E3:3"/>
(  <a href="matrix_1.html#K11" title="MATRIX_1:func.11">0.</a> <font color="Maroon" title="c2">K</font>,<font color="Maroon" title="c1">n</font> is  <a href="matrix_8.html#V1" title="MATRIX_8:attr.1">Idempotent</a>  &amp;  <a href="matrix_1.html#K11" title="MATRIX_1:func.11">0.</a> <font color="Maroon" title="c2">K</font>,<font color="Maroon" title="c1">n</font> is  <a href="matrix_8.html#V2" title="MATRIX_8:attr.2">Nilpotent</a>  )
 <span class="kw">by</span> <span class="lab"><a class="ref" href="matrix_8.html#D1" target="_self" title="MATRIX_8:def.1">Def1</a>, <a class="ref" href="matrix_8.html#D2" target="_self" title="MATRIX_8:def.2">Def2</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/>


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