Jump to navigation Jump to search

General

Display information for equation id:math.234985.2 on revision:234985

* Page found: Quotient space (linear algebra) (eq math.234985.2)

(force rerendering)

Occurrences on the following pages:

Hash: adafa13588ac6efe0dd341edfd992813

TeX (original user input):

\mathrm{codim}(U) = \dim(V/U) = \dim(V) - \dim(U).

TeX (checked):

\mathrm {codim} (U)=\dim(V/U)=\dim(V)-\dim(U).

LaTeXML (experimental; uses MathML) rendering

MathML (5.287 KB / 926 B) :

codim ( U ) = dim ( V / U ) = dim ( V ) - dim ( U ) . codim 𝑈 dimension 𝑉 𝑈 dimension 𝑉 dimension 𝑈 {\displaystyle{\mathrm{codim}}(U)=\dim(V/U)=\dim(V)-\dim(U).}
<math xmlns="http://www.w3.org/1998/Math/MathML" id="p1.1.m1.1" class="ltx_Math" alttext="{\displaystyle{\mathrm{codim}}(U)=\dim(V/U)=\dim(V)-\dim(U).}" display="inline">
  <semantics id="p1.1.m1.1a">
    <mrow id="p1.1.m1.1.27" xref="p1.1.m1.1.27.2.cmml">
      <mrow id="p1.1.m1.1.27.2" xref="p1.1.m1.1.27.2.cmml">
        <mrow id="p1.1.m1.1.27.2.2" xref="p1.1.m1.1.27.2.2.cmml">
          <mi id="p1.1.m1.1.5" xref="p1.1.m1.1.5.cmml">codim</mi>
          <mo id="p1.1.m1.1.27.2.2.1" xref="p1.1.m1.1.27.2.2.1.cmml"></mo>
          <mrow id="p1.1.m1.1.27.2.2.2" xref="p1.1.m1.1.27.2.2.cmml">
            <mo stretchy="false" id="p1.1.m1.1.6" xref="p1.1.m1.1.27.2.2.cmml">(</mo>
            <mi id="p1.1.m1.1.7" xref="p1.1.m1.1.7.cmml">U</mi>
            <mo stretchy="false" id="p1.1.m1.1.8" xref="p1.1.m1.1.27.2.2.cmml">)</mo>
          </mrow>
        </mrow>
        <mo id="p1.1.m1.1.9" xref="p1.1.m1.1.9.cmml">=</mo>
        <mrow id="p1.1.m1.1.27.2.3" xref="p1.1.m1.1.27.2.3.cmml">
          <mo id="p1.1.m1.1.10" xref="p1.1.m1.1.10.cmml">dim</mo>
          <mo id="p1.1.m1.1.27.2.3a" xref="p1.1.m1.1.27.2.3.cmml"></mo>
          <mrow id="p1.1.m1.1.27.2.3.1" xref="p1.1.m1.1.27.2.3.1.2.cmml">
            <mo stretchy="false" id="p1.1.m1.1.11" xref="p1.1.m1.1.27.2.3.1.2.cmml">(</mo>
            <mrow id="p1.1.m1.1.27.2.3.1.2" xref="p1.1.m1.1.27.2.3.1.2.cmml">
              <mi id="p1.1.m1.1.12" xref="p1.1.m1.1.12.cmml">V</mi>
              <mo id="p1.1.m1.1.13" xref="p1.1.m1.1.13.cmml">/</mo>
              <mi id="p1.1.m1.1.14" xref="p1.1.m1.1.14.cmml">U</mi>
            </mrow>
            <mo stretchy="false" id="p1.1.m1.1.15" xref="p1.1.m1.1.27.2.3.1.2.cmml">)</mo>
          </mrow>
        </mrow>
        <mo id="p1.1.m1.1.16" xref="p1.1.m1.1.16.cmml">=</mo>
        <mrow id="p1.1.m1.1.27.2.4" xref="p1.1.m1.1.27.2.4.cmml">
          <mrow id="p1.1.m1.1.27.2.4.1" xref="p1.1.m1.1.27.2.4.1.cmml">
            <mo id="p1.1.m1.1.17" xref="p1.1.m1.1.17.cmml">dim</mo>
            <mo id="p1.1.m1.1.27.2.4.1a" xref="p1.1.m1.1.27.2.4.1.cmml"></mo>
            <mrow id="p1.1.m1.1.27.2.4.1.1" xref="p1.1.m1.1.27.2.4.1.cmml">
              <mo stretchy="false" id="p1.1.m1.1.18" xref="p1.1.m1.1.27.2.4.1.cmml">(</mo>
              <mi id="p1.1.m1.1.19" xref="p1.1.m1.1.19.cmml">V</mi>
              <mo stretchy="false" id="p1.1.m1.1.20" xref="p1.1.m1.1.27.2.4.1.cmml">)</mo>
            </mrow>
          </mrow>
          <mo id="p1.1.m1.1.21" xref="p1.1.m1.1.21.cmml">-</mo>
          <mrow id="p1.1.m1.1.27.2.4.2" xref="p1.1.m1.1.27.2.4.2.cmml">
            <mo id="p1.1.m1.1.22" xref="p1.1.m1.1.22.cmml">dim</mo>
            <mo id="p1.1.m1.1.27.2.4.2a" xref="p1.1.m1.1.27.2.4.2.cmml"></mo>
            <mrow id="p1.1.m1.1.27.2.4.2.1" xref="p1.1.m1.1.27.2.4.2.cmml">
              <mo stretchy="false" id="p1.1.m1.1.23" xref="p1.1.m1.1.27.2.4.2.cmml">(</mo>
              <mi id="p1.1.m1.1.24" xref="p1.1.m1.1.24.cmml">U</mi>
              <mo stretchy="false" id="p1.1.m1.1.25" xref="p1.1.m1.1.27.2.4.2.cmml">)</mo>
            </mrow>
          </mrow>
        </mrow>
      </mrow>
      <mo id="p1.1.m1.1.26" xref="p1.1.m1.1.27.2.cmml">.</mo>
    </mrow>
    <annotation-xml encoding="MathML-Content" id="p1.1.m1.1b">
      <apply id="p1.1.m1.1.27.2.cmml" xref="p1.1.m1.1.27">
        <and id="p1.1.m1.1.27.2a.cmml" xref="p1.1.m1.1.27"/>
        <apply id="p1.1.m1.1.27.2b.cmml" xref="p1.1.m1.1.27">
          <eq id="p1.1.m1.1.9.cmml" xref="p1.1.m1.1.9"/>
          <apply id="p1.1.m1.1.27.2.2.cmml" xref="p1.1.m1.1.27.2.2">
            <times id="p1.1.m1.1.27.2.2.1.cmml" xref="p1.1.m1.1.27.2.2.1"/>
            <ci id="p1.1.m1.1.5.cmml" xref="p1.1.m1.1.5">codim</ci>
            <ci id="p1.1.m1.1.7.cmml" xref="p1.1.m1.1.7">𝑈</ci>
          </apply>
          <apply id="p1.1.m1.1.27.2.3.cmml" xref="p1.1.m1.1.27.2.3">
            <csymbol cd="latexml" id="p1.1.m1.1.10.cmml" xref="p1.1.m1.1.10">dimension</csymbol>
            <apply id="p1.1.m1.1.27.2.3.1.2.cmml" xref="p1.1.m1.1.27.2.3.1">
              <divide id="p1.1.m1.1.13.cmml" xref="p1.1.m1.1.13"/>
              <ci id="p1.1.m1.1.12.cmml" xref="p1.1.m1.1.12">𝑉</ci>
              <ci id="p1.1.m1.1.14.cmml" xref="p1.1.m1.1.14">𝑈</ci>
            </apply>
          </apply>
        </apply>
        <apply id="p1.1.m1.1.27.2c.cmml" xref="p1.1.m1.1.27">
          <eq id="p1.1.m1.1.16.cmml" xref="p1.1.m1.1.16"/>
          <share href="#p1.1.m1.1.27.2.3.cmml" id="p1.1.m1.1.27.2d.cmml" xref="p1.1.m1.1.27"/>
          <apply id="p1.1.m1.1.27.2.4.cmml" xref="p1.1.m1.1.27.2.4">
            <minus id="p1.1.m1.1.21.cmml" xref="p1.1.m1.1.21"/>
            <apply id="p1.1.m1.1.27.2.4.1.cmml" xref="p1.1.m1.1.27.2.4.1">
              <csymbol cd="latexml" id="p1.1.m1.1.17.cmml" xref="p1.1.m1.1.17">dimension</csymbol>
              <ci id="p1.1.m1.1.19.cmml" xref="p1.1.m1.1.19">𝑉</ci>
            </apply>
            <apply id="p1.1.m1.1.27.2.4.2.cmml" xref="p1.1.m1.1.27.2.4.2">
              <csymbol cd="latexml" id="p1.1.m1.1.22.cmml" xref="p1.1.m1.1.22">dimension</csymbol>
              <ci id="p1.1.m1.1.24.cmml" xref="p1.1.m1.1.24">𝑈</ci>
            </apply>
          </apply>
        </apply>
      </apply>
    </annotation-xml>
    <annotation encoding="application/x-tex" id="p1.1.m1.1c">{\displaystyle{\mathrm{codim}}(U)=\dim(V/U)=\dim(V)-\dim(U).}</annotation>
  </semantics>
</math>

SVG (9.914 KB / 3.214 KB) :

c o d i m times left-parenthesis upper U right-parenthesis equals dimension left-parenthesis upper V slash upper U right-parenthesis equals dimension left-parenthesis upper V right-parenthesis minus dimension left-parenthesis upper U right-parenthesis period

SVG (MathML can be enabled via browser plugin) rendering

MathML (1.373 KB / 395 B) :

c o d i m ( U ) = dim ( V / U ) = dim ( V ) dim ( U ) . {\displaystyle \mathrm {codim} (U)=\dim(V/U)=\dim(V)-\dim(U).}
<math xmlns="http://www.w3.org/1998/Math/MathML" display="block" alttext="{\displaystyle \mathrm {codim} (U)=\dim(V/U)=\dim(V)-\dim(U).}">
  <semantics>
    <mrow class="MJX-TeXAtom-ORD">
      <mstyle displaystyle="true" scriptlevel="0">
        <mrow class="MJX-TeXAtom-ORD">
          <mi mathvariant="normal">c</mi>
          <mi mathvariant="normal">o</mi>
          <mi mathvariant="normal">d</mi>
          <mi mathvariant="normal">i</mi>
          <mi mathvariant="normal">m</mi>
        </mrow>
        <mo stretchy="false">(</mo>
        <mi>U</mi>
        <mo stretchy="false">)</mo>
        <mo>=</mo>
        <mi>dim</mi>
        <mo>&#x2061;<!-- ⁡ --></mo>
        <mo stretchy="false">(</mo>
        <mi>V</mi>
        <mrow class="MJX-TeXAtom-ORD">
          <mo>/</mo>
        </mrow>
        <mi>U</mi>
        <mo stretchy="false">)</mo>
        <mo>=</mo>
        <mi>dim</mi>
        <mo>&#x2061;<!-- ⁡ --></mo>
        <mo stretchy="false">(</mo>
        <mi>V</mi>
        <mo stretchy="false">)</mo>
        <mo>&#x2212;<!-- − --></mo>
        <mi>dim</mi>
        <mo>&#x2061;<!-- ⁡ --></mo>
        <mo stretchy="false">(</mo>
        <mi>U</mi>
        <mo stretchy="false">)</mo>
        <mo>.</mo>
      </mstyle>
    </mrow>
    <annotation encoding="application/x-tex">{\displaystyle \mathrm {codim} (U)=\dim(V/U)=\dim(V)-\dim(U).}</annotation>
  </semantics>
</math>

SVG (7.444 KB / 2.896 KB) :

{\displaystyle \mathrm {codim} (U)=\dim(V/U)=\dim(V)-\dim(U).}

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 Quotient space (linear algebra) page

Identifiers

MathML observations

0results

0results

no statistics present please run the maintenance script ExtractFeatures.php

0 results

0 results