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<div><span class="kw">theorem </span><span class="lab"><font color="Green" title="E14">Th14</font></span>: <a NAME="T14"><span class="comment"><font color="firebrick">:: VECTSP11:14</font></span><br/></a><div class="add"> for <font color="Olive" title="b1">K</font> being   <a href="vectsp_1.html#NM5" title="VECTSP_1:NM.5">Field</a><br/>  for <font color="Olive" title="b2">V1</font> being   <a href="vectsp_1.html#NM9" title="VECTSP_1:NM.9">VectSp</a> of <font color="Olive" title="b1">K</font><br/>  for <font color="Olive" title="b3">f</font> being   <a href="ranknull.html#NM1" title="RANKNULL:NM.1">linear-transformation</a> of <font color="Olive" title="b2">V1</font>,<font color="Olive" title="b2">V1</font><br/>  for <font color="Olive" title="b4">L</font> being   <a href="vectsp_1.html#NM6" title="VECTSP_1:NM.6">Scalar</a> of <font color="Olive" title="b1">K</font> holds <br/> ( ( <font color="Olive" title="b3">f</font> is  <a href="vectsp11.html#V1" title="VECTSP11:attr.1">with_eigenvalues</a>  &amp; <font color="Olive" title="b4">L</font> is    <a href="vectsp11.html#M1" title="VECTSP11:mode.1">eigenvalue</a> of <font color="Olive" title="b3">f</font> ) iff  not  <a href="ranknull.html#K1" title="RANKNULL:func.1">ker</a> <span class="p1">(<span class="default"><font color="Olive" title="b3">f</font> <a href="matrlin.html#K3" title="MATRLIN:func.3">+</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="algstr_0.html#K4" title="ALGSTR_0:func.4">-</a> <font color="Olive" title="b4">L</font></span>)</span> <a href="matrlin.html#K4" title="MATRLIN:func.4">*</a> <span class="p3">(<span class="default"><a href="struct_0.html#K3" title="STRUCT_0:func.3">id</a> <font color="Olive" title="b2">V1</font></span>)</span></span>)</span></span>)</span> is  <a href="struct_0.html#V7" title="STRUCT_0:attr.7">trivial</a>  )</div></div>
