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<div><span class="kw">theorem </span><a NAME="T6"><span class="comment"><font color="firebrick">:: MATRIX_8:6</font></span><br/></a><div class="add"> for <font color="Olive" title="b1">n</font> being   <a href="ordinal1.html#NM6" title="ORDINAL1:NM.6">Nat</a><br/>  for <font color="Olive" title="b2">K</font> being   <a href="vectsp_1.html#NM5" title="VECTSP_1:NM.5">Field</a><br/>  for <font color="Olive" title="b3">M1</font>, <font color="Olive" title="b4">M2</font> being   <a href="matrix_1.html#NM2" title="MATRIX_1:NM.2">Matrix</a> of <font color="Olive" title="b1">n</font>,<font color="Olive" title="b2">K</font>  st <font color="Olive" title="b1">n</font> <a href="xxreal_0.html#NR4" title="XXREAL_0:NR.4">&gt;</a>  <a href="numbers.html#K5" title="NUMBERS:func.5">0</a>  &amp; <font color="Olive" title="b3">M1</font> is  <a href="matrix_8.html#V1" title="MATRIX_8:attr.1">Idempotent</a>  &amp; <font color="Olive" title="b4">M2</font> is  <a href="matrix_8.html#V1" title="MATRIX_8:attr.1">Idempotent</a>  &amp; <font color="Olive" title="b3">M1</font> <a href="matrix_6.html#R1" title="MATRIX_6:pred.1">commutes_with</a> <font color="Olive" title="b4">M2</font> &amp; <font color="Olive" title="b3">M1</font> <a href="matrix_3.html#K4" title="MATRIX_3:func.4">*</a> <font color="Olive" title="b4">M2</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="matrix_1.html#K2" title="MATRIX_1:func.2">0.</a> (<font color="Olive" title="b2">K</font>,<font color="Olive" title="b1">n</font>) holds <br/><font color="Olive" title="b3">M1</font> <a href="matrix_3.html#K3" title="MATRIX_3:func.3">+</a> <font color="Olive" title="b4">M2</font> is  <a href="matrix_8.html#V1" title="MATRIX_8:attr.1">Idempotent</a> </div></div>
