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mathmlben

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Visualization for goldstandard

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<math xmlns="http://www.w3.org/1998/Math/MathML" display="block" alttext="Start 2 By 3 Matrix 1st Row 1st Column j 1 2nd Column j 2 3rd Column j 3 2nd Row 1st Column m 1 2nd Column m 2 3rd Column m 3 EndMatrix equals left-parenthesis negative 1 right-parenthesis Superscript j 1 plus j 2 plus j 3 Baseline Start 2 By 3 Matrix 1st Row 1st Column j 1 2nd Column j 2 3rd Column j 3 2nd Row 1st Column minus m 1 2nd Column minus m 2 3rd Column minus m 3 EndMatrix"> <semantics> <mrow data-semantic-type="relseq" data-semantic-role="equality" data-semantic-id="88" data-semantic-children="27,87" data-semantic-content="30"> <mrow class="MJX-TeXAtom-ORD"> <mrow data-semantic-type="matrix" data-semantic-role="unknown" data-semantic-id="27" data-semantic-children="13,26" data-semantic-content="0,28" data-semantic-parent="88"> <mo data-semantic-type="fence" data-semantic-role="open" data-semantic-id="0" data-semantic-parent="27">(</mo> <mtable rowspacing="4pt" columnspacing="1em"> <mtr data-semantic-type="row" data-semantic-role="matrix" data-semantic-id="13" data-semantic-children="4,8,12" data-semantic-parent="27"> <mtd data-semantic-type="cell" data-semantic-role="matrix" data-semantic-id="4" data-semantic-children="3" data-semantic-parent="13"> <msub data-semantic-type="subscript" data-semantic-role="latinletter" data-semantic-id="3" data-semantic-children="1,2" data-semantic-parent="4"> <mi data-semantic-type="identifier" data-semantic-role="latinletter" data-semantic-font="italic" data-semantic-id="1" data-semantic-parent="3">j</mi> <mrow class="MJX-TeXAtom-ORD"> <mn data-semantic-type="number" data-semantic-role="integer" data-semantic-font="normal" data-semantic-id="2" data-semantic-parent="3">1</mn> </mrow> </msub> </mtd> <mtd data-semantic-type="cell" data-semantic-role="matrix" data-semantic-id="8" data-semantic-children="7" data-semantic-parent="13"> <msub data-semantic-type="subscript" data-semantic-role="latinletter" data-semantic-id="7" data-semantic-children="5,6" data-semantic-parent="8"> <mi data-semantic-type="identifier" data-semantic-role="latinletter" data-semantic-font="italic" data-semantic-id="5" data-semantic-parent="7">j</mi> <mrow class="MJX-TeXAtom-ORD"> <mn data-semantic-type="number" data-semantic-role="integer" data-semantic-font="normal" data-semantic-id="6" data-semantic-parent="7">2</mn> </mrow> </msub> </mtd> <mtd data-semantic-type="cell" data-semantic-role="matrix" data-semantic-id="12" data-semantic-children="11" data-semantic-parent="13"> <msub data-semantic-type="subscript" data-semantic-role="latinletter" data-semantic-id="11" data-semantic-children="9,10" data-semantic-parent="12"> <mi data-semantic-type="identifier" data-semantic-role="latinletter" data-semantic-font="italic" data-semantic-id="9" data-semantic-parent="11">j</mi> <mrow class="MJX-TeXAtom-ORD"> <mn data-semantic-type="number" data-semantic-role="integer" data-semantic-font="normal" data-semantic-id="10" data-semantic-parent="11">3</mn> </mrow> </msub> </mtd> </mtr> <mtr data-semantic-type="row" data-semantic-role="matrix" data-semantic-id="26" data-semantic-children="17,21,25" data-semantic-parent="27"> <mtd data-semantic-type="cell" data-semantic-role="matrix" data-semantic-id="17" data-semantic-children="16" data-semantic-parent="26"> <msub data-semantic-type="subscript" data-semantic-role="latinletter" data-semantic-id="16" data-semantic-children="14,15" data-semantic-parent="17"> <mi data-semantic-type="identifier" data-semantic-role="latinletter" data-semantic-font="italic" data-semantic-id="14" data-semantic-parent="16">m</mi> <mrow class="MJX-TeXAtom-ORD"> <mn data-semantic-type="number" data-semantic-role="integer" data-semantic-font="normal" data-semantic-id="15" data-semantic-parent="16">1</mn> </mrow> </msub> </mtd> <mtd data-semantic-type="cell" data-semantic-role="matrix" data-semantic-id="21" data-semantic-children="20" data-semantic-parent="26"> <msub data-semantic-type="subscript" data-semantic-role="latinletter" data-semantic-id="20" data-semantic-children="18,19" data-semantic-parent="21"> <mi data-semantic-type="identifier" data-semantic-role="latinletter" data-semantic-font="italic" data-semantic-id="18" data-semantic-parent="20">m</mi> <mrow class="MJX-TeXAtom-ORD"> <mn data-semantic-type="number" data-semantic-role="integer" data-semantic-font="normal" data-semantic-id="19" data-semantic-parent="20">2</mn> </mrow> </msub> </mtd> <mtd data-semantic-type="cell" data-semantic-role="matrix" data-semantic-id="25" data-semantic-children="24" data-semantic-parent="26"> <msub data-semantic-type="subscript" data-semantic-role="latinletter" data-semantic-id="24" data-semantic-children="22,23" data-semantic-parent="25"> <mi data-semantic-type="identifier" data-semantic-role="latinletter" data-semantic-font="italic" data-semantic-id="22" data-semantic-parent="24">m</mi> <mrow class="MJX-TeXAtom-ORD"> <mn data-semantic-type="number" data-semantic-role="integer" data-semantic-font="normal" data-semantic-id="23" data-semantic-parent="24">3</mn> </mrow> </msub> </mtd> </mtr> </mtable> <mo data-semantic-type="fence" data-semantic-role="close" data-semantic-id="28" data-semantic-parent="27">)</mo> </mrow> </mrow> <mo data-semantic-type="relation" data-semantic-role="equality" data-semantic-id="30" data-semantic-parent="88" data-semantic-operator="relseq,=">=</mo> <mrow data-semantic-type="infixop" data-semantic-role="implicit" data-semantic-id="87" data-semantic-children="47,81" data-semantic-content="86" data-semantic-parent="88"> <msup data-semantic-type="superscript" data-semantic-role="leftright" data-semantic-id="47" data-semantic-children="85,46" data-semantic-parent="87" data-semantic-fencepointer="34"> <mrow data-semantic-type="fenced" data-semantic-role="leftright" data-semantic-id="85" data-semantic-children="84" data-semantic-content="31,34" data-semantic-parent="47"> <mo stretchy="false" data-semantic-type="fence" data-semantic-role="open" data-semantic-id="31" data-semantic-parent="85">(</mo> <mrow data-semantic-type="prefixop" data-semantic-role="negative" data-semantic-id="84" data-semantic-children="33" data-semantic-content="32" data-semantic-parent="85"> <mo data-semantic-type="operator" data-semantic-role="subtraction" data-semantic-id="32" data-semantic-parent="84" data-semantic-operator="prefixop,−"><!-- − --> </mo> <mn data-semantic-type="number" data-semantic-role="integer" data-semantic-font="normal" data-semantic-id="33" data-semantic-parent="84">1</mn> </mrow> <mo stretchy="false" data-semantic-type="fence" data-semantic-role="close" data-semantic-id="34" data-semantic-parent="85">)</mo> </mrow> <mrow class="MJX-TeXAtom-ORD" data-semantic-type="infixop" data-semantic-role="addition" data-semantic-id="46" data-semantic-children="37,41,45" data-semantic-content="38,42" data-semantic-parent="47"> <msub data-semantic-type="subscript" data-semantic-role="latinletter" data-semantic-id="37" data-semantic-children="35,36" data-semantic-parent="46"> <mi data-semantic-type="identifier" data-semantic-role="latinletter" data-semantic-font="italic" data-semantic-id="35" data-semantic-parent="37">j</mi> <mrow class="MJX-TeXAtom-ORD"> <mn data-semantic-type="number" data-semantic-role="integer" data-semantic-font="normal" data-semantic-id="36" data-semantic-parent="37">1</mn> </mrow> </msub> <mo data-semantic-type="operator" data-semantic-role="addition" data-semantic-id="38" data-semantic-parent="46" data-semantic-operator="infixop,+">+</mo> <msub data-semantic-type="subscript" data-semantic-role="latinletter" data-semantic-id="41" data-semantic-children="39,40" data-semantic-parent="46"> <mi data-semantic-type="identifier" data-semantic-role="latinletter" data-semantic-font="italic" data-semantic-id="39" data-semantic-parent="41">j</mi> <mrow class="MJX-TeXAtom-ORD"> <mn data-semantic-type="number" data-semantic-role="integer" data-semantic-font="normal" data-semantic-id="40" data-semantic-parent="41">2</mn> </mrow> </msub> <mo data-semantic-type="operator" data-semantic-role="addition" data-semantic-id="42" data-semantic-parent="46" data-semantic-operator="infixop,+">+</mo> <msub data-semantic-type="subscript" data-semantic-role="latinletter" data-semantic-id="45" data-semantic-children="43,44" data-semantic-parent="46"> <mi data-semantic-type="identifier" data-semantic-role="latinletter" data-semantic-font="italic" data-semantic-id="43" data-semantic-parent="45">j</mi> <mrow class="MJX-TeXAtom-ORD"> <mn data-semantic-type="number" data-semantic-role="integer" data-semantic-font="normal" data-semantic-id="44" data-semantic-parent="45">3</mn> </mrow> </msub> </mrow> </msup> <mo data-semantic-type="operator" data-semantic-role="multiplication" data-semantic-id="86" data-semantic-parent="87" data-semantic-added="true" data-semantic-operator="infixop,⁢"></mo> <mrow class="MJX-TeXAtom-ORD"> <mrow data-semantic-type="matrix" data-semantic-role="unknown" data-semantic-id="81" data-semantic-children="61,80" data-semantic-content="48,82" data-semantic-parent="87"> <mo data-semantic-type="fence" data-semantic-role="open" data-semantic-id="48" data-semantic-parent="81">(</mo> <mtable rowspacing="4pt" columnspacing="1em"> <mtr data-semantic-type="row" data-semantic-role="matrix" data-semantic-id="61" data-semantic-children="52,56,60" data-semantic-parent="81"> <mtd data-semantic-type="cell" data-semantic-role="matrix" data-semantic-id="52" data-semantic-children="51" data-semantic-parent="61"> <msub data-semantic-type="subscript" data-semantic-role="latinletter" data-semantic-id="51" data-semantic-children="49,50" data-semantic-parent="52"> <mi data-semantic-type="identifier" data-semantic-role="latinletter" data-semantic-font="italic" data-semantic-id="49" data-semantic-parent="51">j</mi> <mrow class="MJX-TeXAtom-ORD"> <mn data-semantic-type="number" data-semantic-role="integer" data-semantic-font="normal" data-semantic-id="50" data-semantic-parent="51">1</mn> </mrow> </msub> </mtd> <mtd data-semantic-type="cell" data-semantic-role="matrix" data-semantic-id="56" data-semantic-children="55" data-semantic-parent="61"> <msub data-semantic-type="subscript" data-semantic-role="latinletter" data-semantic-id="55" data-semantic-children="53,54" data-semantic-parent="56"> <mi data-semantic-type="identifier" data-semantic-role="latinletter" data-semantic-font="italic" data-semantic-id="53" data-semantic-parent="55">j</mi> <mrow class="MJX-TeXAtom-ORD"> <mn data-semantic-type="number" data-semantic-role="integer" data-semantic-font="normal" data-semantic-id="54" data-semantic-parent="55">2</mn> </mrow> </msub> </mtd> <mtd data-semantic-type="cell" data-semantic-role="matrix" data-semantic-id="60" data-semantic-children="59" data-semantic-parent="61"> <msub data-semantic-type="subscript" data-semantic-role="latinletter" data-semantic-id="59" data-semantic-children="57,58" data-semantic-parent="60"> <mi data-semantic-type="identifier" data-semantic-role="latinletter" data-semantic-font="italic" data-semantic-id="57" data-semantic-parent="59">j</mi> <mrow class="MJX-TeXAtom-ORD"> <mn data-semantic-type="number" data-semantic-role="integer" data-semantic-font="normal" data-semantic-id="58" data-semantic-parent="59">3</mn> </mrow> </msub> </mtd> </mtr> <mtr data-semantic-type="row" data-semantic-role="matrix" data-semantic-id="80" data-semantic-children="67,73,79" data-semantic-parent="81"> <mtd data-semantic-type="cell" data-semantic-role="matrix" data-semantic-id="67" data-semantic-children="66" data-semantic-parent="80"> <mrow data-semantic-type="prefixop" data-semantic-role="negative" data-semantic-id="66" data-semantic-children="65" data-semantic-content="62" data-semantic-parent="67"> <mo data-semantic-type="operator" data-semantic-role="subtraction" data-semantic-id="62" data-semantic-parent="66" data-semantic-operator="prefixop,−"><!-- − --> </mo> <msub data-semantic-type="subscript" data-semantic-role="latinletter" data-semantic-id="65" data-semantic-children="63,64" data-semantic-parent="66"> <mi data-semantic-type="identifier" data-semantic-role="latinletter" data-semantic-font="italic" data-semantic-id="63" data-semantic-parent="65">m</mi> <mrow class="MJX-TeXAtom-ORD"> <mn data-semantic-type="number" data-semantic-role="integer" data-semantic-font="normal" data-semantic-id="64" data-semantic-parent="65">1</mn> </mrow> </msub> </mrow> </mtd> <mtd data-semantic-type="cell" data-semantic-role="matrix" data-semantic-id="73" data-semantic-children="72" data-semantic-parent="80"> <mrow data-semantic-type="prefixop" data-semantic-role="negative" data-semantic-id="72" data-semantic-children="71" data-semantic-content="68" data-semantic-parent="73"> <mo data-semantic-type="operator" data-semantic-role="subtraction" data-semantic-id="68" data-semantic-parent="72" data-semantic-operator="prefixop,−"><!-- − --> </mo> <msub data-semantic-type="subscript" data-semantic-role="latinletter" data-semantic-id="71" data-semantic-children="69,70" data-semantic-parent="72"> <mi data-semantic-type="identifier" data-semantic-role="latinletter" data-semantic-font="italic" data-semantic-id="69" data-semantic-parent="71">m</mi> <mrow class="MJX-TeXAtom-ORD"> <mn data-semantic-type="number" data-semantic-role="integer" data-semantic-font="normal" data-semantic-id="70" data-semantic-parent="71">2</mn> </mrow> </msub> </mrow> </mtd> <mtd data-semantic-type="cell" data-semantic-role="matrix" data-semantic-id="79" data-semantic-children="78" data-semantic-parent="80"> <mrow data-semantic-type="prefixop" data-semantic-role="negative" data-semantic-id="78" data-semantic-children="77" data-semantic-content="74" data-semantic-parent="79"> <mo data-semantic-type="operator" data-semantic-role="subtraction" data-semantic-id="74" data-semantic-parent="78" data-semantic-operator="prefixop,−"><!-- − --> </mo> <msub data-semantic-type="subscript" data-semantic-role="latinletter" data-semantic-id="77" data-semantic-children="75,76" data-semantic-parent="78"> <mi data-semantic-type="identifier" data-semantic-role="latinletter" data-semantic-font="italic" data-semantic-id="75" data-semantic-parent="77">m</mi> <mrow class="MJX-TeXAtom-ORD"> <mn data-semantic-type="number" data-semantic-role="integer" data-semantic-font="normal" data-semantic-id="76" data-semantic-parent="77">3</mn> </mrow> </msub> </mrow> </mtd> </mtr> </mtable> <mo data-semantic-type="fence" data-semantic-role="close" data-semantic-id="82" data-semantic-parent="81">)</mo> </mrow> </mrow> </mrow> </mrow> <annotation encoding="application/x-tex">{\begin{pmatrix}j_{1}&amp;j_{2}&amp;j_{3}\\m_{1}&amp;m_{2}&amp;m_{3}\end{pmatrix}}=(-1)^{j_{1}+j_{2}+j_{3}}{\begin{pmatrix}j_{1}&amp;j_{2}&amp;j_{3}\\-m_{1}&amp;-m_{2}&amp;-m_{3}\end{pmatrix}}</annotation> </semantics> </math>