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<b>let </b><font color="Maroon" title="c1">n</font> be    <a href="subset_1.html#M2" title="SUBSET_1:mode.2">Element</a> of  <a href="numbers.html#K5" title="NUMBERS:func.5">NAT</a> ;<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>;<br/><b>let </b><font color="Maroon" title="c3">M</font> be    <a href="matrix_2.html#M2" title="MATRIX_2:mode.2">Lower_Triangular_Matrix</a> of <font color="Maroon" title="c1">n</font>,<font color="Maroon" title="c2">K</font>;<br/>





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(  <a href="matrix_3.html#K12" title="MATRIX_3:func.12">Det</a> <font color="Maroon" title="c3">M</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="matrix_3.html#K12" title="MATRIX_3:func.12">Det</a> <span class="p1">(<span class="default"><font color="Maroon" title="c3">M</font> <a href="matrix_7.html#K4" title="MATRIX_7:func.4">@</a> </span>)</span> &amp; <font color="Maroon" title="c3">M</font> <a href="matrix_7.html#K4" title="MATRIX_7:func.4">@</a>  is    <a href="matrix_2.html#M1" title="MATRIX_2:mode.1">Upper_Triangular_Matrix</a> of <font color="Maroon" title="c1">n</font>,<font color="Maroon" title="c2">K</font> )
 
<b>by </b><i><a class="ref" href="matrixr2.html#T43" title="MATRIXR2:th.43">MATRIXR2:43</a>, <a class="ref" href="matrix13.html#T2" target="_self" title="MATRIX13:th.2">TT1</a></i>;<br/>
<b>hence </b> <a href="matrix_3.html#K12" title="MATRIX_3:func.12">Det</a> <font color="Maroon" title="c3">M</font> = 
the <a href="group_1.html#U1" title="GROUP_1:sel.1">mult</a> of <font color="Maroon" title="c2">K</font> <a href="finsop_1.html#K2" title="FINSOP_1:func.2">$$</a> <span class="p1">(<span class="default"><a href="matrix_3.html#K13" title="MATRIX_3:func.13">diagonal_of_Matrix</a> <span class="p2">(<span class="default"><font color="Maroon" title="c3">M</font> <a href="matrix_7.html#K4" title="MATRIX_7:func.4">@</a> </span>)</span></span>)</span>
<b>by </b><i><a class="ref" href="matrix13.html#T7" target="_self" title="MATRIX13:th.7">TT6</a></i>
<br/>.= 
the <a href="group_1.html#U1" title="GROUP_1:sel.1">mult</a> of <font color="Maroon" title="c2">K</font> <a href="finsop_1.html#K2" title="FINSOP_1:func.2">$$</a> <span class="p1">(<span class="default"><a href="matrix_3.html#K13" title="MATRIX_3:func.13">diagonal_of_Matrix</a> <font color="Maroon" title="c3">M</font></span>)</span>
<b>by </b><i><a class="ref" href="matrix13.html#T3" target="_self" title="MATRIX13:th.3">TT2</a></i>
;<br/><br/>


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