Jump to navigation Jump to search

General

Display information for equation id:math.225608.24 on revision:225608

* Page found: Hermitian matrix (eq math.225608.24)

(force rerendering)

Cannot find the equation data in the database. Fetching from revision text.

Occurrences on the following pages:

Hash: 2cf3fe456a4e63e36fdd339faa275cf6

TeX (original user input):

 A = \sum _j \lambda_j u_j u_j ^\dagger

LaTeXML (experimental; uses MathML) rendering

MathML (4.089 KB / 827 B) :

A = j λ j u j u j 𝐴 subscript 𝑗 subscript 𝜆 𝑗 subscript 𝑢 𝑗 superscript subscript 𝑢 𝑗 {\displaystyle A=\sum_{j}\lambda_{j}u_{j}u_{j}^{\dagger}}
<math xmlns="http://www.w3.org/1998/Math/MathML" id="p1.1.m1.1" class="ltx_Math" alttext="{\displaystyle A=\sum_{j}\lambda_{j}u_{j}u_{j}^{\dagger}}" display="inline">
  <semantics id="p1.1.m1.1a">
    <mrow id="p1.1.m1.1.12" xref="p1.1.m1.1.12.cmml">
      <mi id="p1.1.m1.1.1" xref="p1.1.m1.1.1.cmml">A</mi>
      <mo id="p1.1.m1.1.2" xref="p1.1.m1.1.2.cmml">=</mo>
      <mrow id="p1.1.m1.1.12.1" xref="p1.1.m1.1.12.1.cmml">
        <mstyle displaystyle="true" id="p1.1.m1.1.12.1.1" xref="p1.1.m1.1.12.1.1.cmml">
          <munder id="p1.1.m1.1.12.1.1a" xref="p1.1.m1.1.12.1.1.cmml">
            <mo largeop="true" movablelimits="false" symmetric="true" id="p1.1.m1.1.3" xref="p1.1.m1.1.3.cmml"></mo>
            <mi id="p1.1.m1.1.4.1" xref="p1.1.m1.1.4.1.cmml">j</mi>
          </munder>
        </mstyle>
        <mrow id="p1.1.m1.1.12.1.2" xref="p1.1.m1.1.12.1.2.cmml">
          <msub id="p1.1.m1.1.12.1.2.2" xref="p1.1.m1.1.12.1.2.2.cmml">
            <mi id="p1.1.m1.1.5" xref="p1.1.m1.1.5.cmml">λ</mi>
            <mi id="p1.1.m1.1.6.1" xref="p1.1.m1.1.6.1.cmml">j</mi>
          </msub>
          <mo id="p1.1.m1.1.12.1.2.1" xref="p1.1.m1.1.12.1.2.1.cmml"></mo>
          <msub id="p1.1.m1.1.12.1.2.3" xref="p1.1.m1.1.12.1.2.3.cmml">
            <mi id="p1.1.m1.1.7" xref="p1.1.m1.1.7.cmml">u</mi>
            <mi id="p1.1.m1.1.8.1" xref="p1.1.m1.1.8.1.cmml">j</mi>
          </msub>
          <mo id="p1.1.m1.1.12.1.2.1a" xref="p1.1.m1.1.12.1.2.1.cmml"></mo>
          <msubsup id="p1.1.m1.1.12.1.2.4" xref="p1.1.m1.1.12.1.2.4.cmml">
            <mi id="p1.1.m1.1.9" xref="p1.1.m1.1.9.cmml">u</mi>
            <mi id="p1.1.m1.1.10.1" xref="p1.1.m1.1.10.1.cmml">j</mi>
            <mo id="p1.1.m1.1.11.1" xref="p1.1.m1.1.11.1.cmml"></mo>
          </msubsup>
        </mrow>
      </mrow>
    </mrow>
    <annotation-xml encoding="MathML-Content" id="p1.1.m1.1b">
      <apply id="p1.1.m1.1.12.cmml" xref="p1.1.m1.1.12">
        <eq id="p1.1.m1.1.2.cmml" xref="p1.1.m1.1.2"/>
        <ci id="p1.1.m1.1.1.cmml" xref="p1.1.m1.1.1">𝐴</ci>
        <apply id="p1.1.m1.1.12.1.cmml" xref="p1.1.m1.1.12.1">
          <apply id="p1.1.m1.1.12.1.1.cmml" xref="p1.1.m1.1.12.1.1">
            <csymbol cd="ambiguous" id="p1.1.m1.1.12.1.1.1.cmml" xref="p1.1.m1.1.12.1.1">subscript</csymbol>
            <sum id="p1.1.m1.1.3.cmml" xref="p1.1.m1.1.3"/>
            <ci id="p1.1.m1.1.4.1.cmml" xref="p1.1.m1.1.4.1">𝑗</ci>
          </apply>
          <apply id="p1.1.m1.1.12.1.2.cmml" xref="p1.1.m1.1.12.1.2">
            <times id="p1.1.m1.1.12.1.2.1.cmml" xref="p1.1.m1.1.12.1.2.1"/>
            <apply id="p1.1.m1.1.12.1.2.2.cmml" xref="p1.1.m1.1.12.1.2.2">
              <csymbol cd="ambiguous" id="p1.1.m1.1.12.1.2.2.1.cmml" xref="p1.1.m1.1.12.1.2.2">subscript</csymbol>
              <ci id="p1.1.m1.1.5.cmml" xref="p1.1.m1.1.5">𝜆</ci>
              <ci id="p1.1.m1.1.6.1.cmml" xref="p1.1.m1.1.6.1">𝑗</ci>
            </apply>
            <apply id="p1.1.m1.1.12.1.2.3.cmml" xref="p1.1.m1.1.12.1.2.3">
              <csymbol cd="ambiguous" id="p1.1.m1.1.12.1.2.3.1.cmml" xref="p1.1.m1.1.12.1.2.3">subscript</csymbol>
              <ci id="p1.1.m1.1.7.cmml" xref="p1.1.m1.1.7">𝑢</ci>
              <ci id="p1.1.m1.1.8.1.cmml" xref="p1.1.m1.1.8.1">𝑗</ci>
            </apply>
            <apply id="p1.1.m1.1.12.1.2.4.cmml" xref="p1.1.m1.1.12.1.2.4">
              <csymbol cd="ambiguous" id="p1.1.m1.1.12.1.2.4.1.cmml" xref="p1.1.m1.1.12.1.2.4">superscript</csymbol>
              <apply id="p1.1.m1.1.12.1.2.4.2.cmml" xref="p1.1.m1.1.12.1.2.4">
                <csymbol cd="ambiguous" id="p1.1.m1.1.12.1.2.4.2.1.cmml" xref="p1.1.m1.1.12.1.2.4">subscript</csymbol>
                <ci id="p1.1.m1.1.9.cmml" xref="p1.1.m1.1.9">𝑢</ci>
                <ci id="p1.1.m1.1.10.1.cmml" xref="p1.1.m1.1.10.1">𝑗</ci>
              </apply>
              <ci id="p1.1.m1.1.11.1.cmml" xref="p1.1.m1.1.11.1"></ci>
            </apply>
          </apply>
        </apply>
      </apply>
    </annotation-xml>
    <annotation encoding="application/x-tex" id="p1.1.m1.1c">{\displaystyle A=\sum_{j}\lambda_{j}u_{j}u_{j}^{\dagger}}</annotation>
  </semantics>
</math>

SVG (6.078 KB / 2.377 KB) :

upper A equals sigma-summation Underscript j Endscripts lamda Subscript j Baseline times u Subscript j Baseline times u Subscript j Superscript dagger

SVG with PNG fallback (MathML can be enabled via browser plugin) rendering

MathML (1.102 KB / 372 B) :

A = j λ j u j u j {\displaystyle A=\sum _{j}\lambda _{j}u_{j}u_{j}^{\dagger }}
<math xmlns="http://www.w3.org/1998/Math/MathML" display="block" alttext="{\displaystyle A=\sum _{j}\lambda _{j}u_{j}u_{j}^{\dagger }}">
  <semantics>
    <mrow class="MJX-TeXAtom-ORD">
      <mstyle displaystyle="true" scriptlevel="0">
        <mi>A</mi>
        <mo>=</mo>
        <munder>
          <mo>&#x2211;<!-- ∑ --></mo>
          <mrow class="MJX-TeXAtom-ORD">
            <mi>j</mi>
          </mrow>
        </munder>
        <msub>
          <mi>&#x03BB;<!-- λ --></mi>
          <mrow class="MJX-TeXAtom-ORD">
            <mi>j</mi>
          </mrow>
        </msub>
        <msub>
          <mi>u</mi>
          <mrow class="MJX-TeXAtom-ORD">
            <mi>j</mi>
          </mrow>
        </msub>
        <msubsup>
          <mi>u</mi>
          <mrow class="MJX-TeXAtom-ORD">
            <mi>j</mi>
          </mrow>
          <mrow class="MJX-TeXAtom-ORD">
            <mo>&#x2020;<!-- † --></mo>
          </mrow>
        </msubsup>
      </mstyle>
    </mrow>
    <annotation encoding="application/x-tex">{\displaystyle A=\sum _{j}\lambda _{j}u_{j}u_{j}^{\dagger }}</annotation>
  </semantics>
</math>

SVG (4.852 KB / 2.178 KB) :

{\displaystyle A=\sum _{j}\lambda _{j}u_{j}u_{j}^{\dagger }}

PNG (0 B / 8 B) :


Translations to Computer Algebra Systems

Translation to Maple

In Maple:

Translation to Mathematica

In Mathematica:

Similar pages

Calculated based on the variables occurring on the entire Hermitian matrix page

Identifiers

MathML observations

0results

0results

no statistics present please run the maintenance script ExtractFeatures.php

0 results

0 results