mathmlben
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Visualization for goldstandard
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text/mathml
<math
xmlns="http://www.w3.org/1998/Math/MathML" display="block" alttext="Ker left-parenthesis k Subscript asterisk Baseline minus l Subscript asterisk Baseline right-parenthesis approximately-equals Im left-parenthesis i Subscript asterisk Baseline comma j Subscript asterisk Baseline right-parenthesis">
<semantics>
<mrow data-semantic-type="punctuated" data-semantic-role="text" data-semantic-id="30" data-semantic-children="0,26,11,24" data-semantic-content="27,28,29">
<mrow class="MJX-TeXAtom-ORD">
<mtext data-semantic-type="text" data-semantic-role="unknown" data-semantic-font="normal" data-semantic-id="0" data-semantic-parent="30">Ker</mtext>
</mrow>
<mo data-semantic-type="punctuation" data-semantic-role="dummy" data-semantic-id="27" data-semantic-parent="30" data-semantic-added="true" data-semantic-operator="punctuated"></mo>
<mrow data-semantic-type="relseq" data-semantic-role="equality" data-semantic-id="26" data-semantic-children="22,25" data-semantic-content="10" data-semantic-parent="30">
<mrow data-semantic-type="fenced" data-semantic-role="leftright" data-semantic-id="22" data-semantic-children="21" data-semantic-content="1,9" data-semantic-parent="26">
<mo stretchy="false" data-semantic-type="fence" data-semantic-role="open" data-semantic-id="1" data-semantic-parent="22" data-semantic-operator="fenced">(</mo>
<mrow data-semantic-type="infixop" data-semantic-role="subtraction" data-semantic-id="21" data-semantic-children="4,8" data-semantic-content="5" data-semantic-parent="22">
<msub data-semantic-type="subscript" data-semantic-role="latinletter" data-semantic-id="4" data-semantic-children="2,3" data-semantic-parent="21">
<mi data-semantic-type="identifier" data-semantic-role="latinletter" data-semantic-font="italic" data-semantic-id="2" data-semantic-parent="4">k</mi>
<mrow class="MJX-TeXAtom-ORD">
<mo data-semantic-type="operator" data-semantic-role="multiplication" data-semantic-id="3" data-semantic-parent="4">∗
<!-- ∗ -->
</mo>
</mrow>
</msub>
<mo data-semantic-type="operator" data-semantic-role="subtraction" data-semantic-id="5" data-semantic-parent="21" data-semantic-operator="infixop,−">−
<!-- − -->
</mo>
<msub data-semantic-type="subscript" data-semantic-role="latinletter" data-semantic-id="8" data-semantic-children="6,7" data-semantic-parent="21">
<mi data-semantic-type="identifier" data-semantic-role="latinletter" data-semantic-font="italic" data-semantic-id="6" data-semantic-parent="8">l</mi>
<mrow class="MJX-TeXAtom-ORD">
<mo data-semantic-type="operator" data-semantic-role="multiplication" data-semantic-id="7" data-semantic-parent="8">∗
<!-- ∗ -->
</mo>
</mrow>
</msub>
</mrow>
<mo stretchy="false" data-semantic-type="fence" data-semantic-role="close" data-semantic-id="9" data-semantic-parent="22" data-semantic-operator="fenced">)</mo>
</mrow>
<mo data-semantic-type="relation" data-semantic-role="equality" data-semantic-id="10" data-semantic-parent="26" data-semantic-operator="relseq,≅">≅
<!-- ≅ -->
</mo>
<mrow data-semantic-type="empty" data-semantic-role="unknown" data-semantic-id="25" data-semantic-parent="26"/></mrow>
<mo data-semantic-type="punctuation" data-semantic-role="dummy" data-semantic-id="28" data-semantic-parent="30" data-semantic-added="true" data-semantic-operator="punctuated"></mo>
<mrow class="MJX-TeXAtom-ORD">
<mtext data-semantic-type="text" data-semantic-role="unknown" data-semantic-font="normal" data-semantic-id="11" data-semantic-parent="30">Im</mtext>
</mrow>
<mo data-semantic-type="punctuation" data-semantic-role="dummy" data-semantic-id="29" data-semantic-parent="30" data-semantic-added="true" data-semantic-operator="punctuated"></mo>
<mrow data-semantic-type="fenced" data-semantic-role="leftright" data-semantic-id="24" data-semantic-children="23" data-semantic-content="12,20" data-semantic-parent="30">
<mo stretchy="false" data-semantic-type="fence" data-semantic-role="open" data-semantic-id="12" data-semantic-parent="24" data-semantic-operator="fenced">(</mo>
<mrow data-semantic-type="punctuated" data-semantic-role="sequence" data-semantic-id="23" data-semantic-children="15,16,19" data-semantic-content="16" data-semantic-parent="24">
<msub data-semantic-type="subscript" data-semantic-role="latinletter" data-semantic-id="15" data-semantic-children="13,14" data-semantic-parent="23">
<mi data-semantic-type="identifier" data-semantic-role="latinletter" data-semantic-font="italic" data-semantic-id="13" data-semantic-parent="15">i</mi>
<mrow class="MJX-TeXAtom-ORD">
<mo data-semantic-type="operator" data-semantic-role="multiplication" data-semantic-id="14" data-semantic-parent="15">∗
<!-- ∗ -->
</mo>
</mrow>
</msub>
<mo data-semantic-type="punctuation" data-semantic-role="comma" data-semantic-id="16" data-semantic-parent="23" data-semantic-operator="punctuated">,</mo>
<msub data-semantic-type="subscript" data-semantic-role="latinletter" data-semantic-id="19" data-semantic-children="17,18" data-semantic-parent="23">
<mi data-semantic-type="identifier" data-semantic-role="latinletter" data-semantic-font="italic" data-semantic-id="17" data-semantic-parent="19">j</mi>
<mrow class="MJX-TeXAtom-ORD">
<mo data-semantic-type="operator" data-semantic-role="multiplication" data-semantic-id="18" data-semantic-parent="19">∗
<!-- ∗ -->
</mo>
</mrow>
</msub>
</mrow>
<mo stretchy="false" data-semantic-type="fence" data-semantic-role="close" data-semantic-id="20" data-semantic-parent="24" data-semantic-operator="fenced">)</mo>
</mrow>
</mrow>
<annotation encoding="application/x-tex">{\text{Ker}}(k_{*}-l_{*})\cong {\text{Im}}(i_{*},j_{*})</annotation>
</semantics>
</math>