Beispiel: Funktionen für Matrixnormen und -determinanten

Funktionen > Vektor und Matrix > Array-Eigenschaften > Beispiel: Funktionen für Matrixnormen und -determinanten

Beispiel: Funktionen für Matrixnormen und -determinanten

1. Definieren Sie eine quadratische Matrix.

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2. Legen Sie die Matrixelemente auf generische Variablennamen fest.

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3. Verwenden Sie die Funktion norm1, um die Norm L1 der Matrix M zu ermitteln.

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Alternativ können Sie die Norm L1 ermitteln, indem Sie das Maximum der absoluten Spaltensummen von M berechnen.

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4. Verwenden Sie die Funktion norm2, um die Norm L2 der Matrix M zu ermitteln.

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Verwenden Sie alternativ die Funktion svds, um den größten absoluten singulären Wert der Matrix M zu ermitteln.

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Die Funktion svds gibt einen Vektor von sortierten singulären Werten zurück, sodass der oberste Wert der größte singuläre Wert der Matrix M ist.

5. Verwenden Sie die Funktion norme, um die Euklid-Norm der Matrix M zu ermitteln.

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Berechnen Sie alternativ manuell die Quadratwurzel der Summe der absoluten Quadrate der Matrix M.

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6. Verwenden Sie die Funktion normi, um die Unendlichnorm der Matrix M zu ermitteln.

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Verwenden Sie alternativ die max-Funktion, um das Maximum der absoluten Zeilensummen der Matrix M manuell zu berechnen.

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          <id labels="VARIABLE" xml:space="preserve" xml:lang="de" label-is-contextual="true">
            <Span xml:lang="de" xmlns="http://schemas.microsoft.com/winfx/2006/xaml/presentation">b<Subscript xml:lang="de" xmlns="clr-namespace:Ptc.Wpf;assembly=Ptc.Core">2</Subscript></Span>
          </id>
        </apply>
      </apply>
    </define>
    <resultFormat xml:lang="de">
      <matrix size="12,12" offset="0,0" show-indices="false" expand-nested-arrays="false" xml:lang="de" />
    </resultFormat>
  </math>
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      <matrix size="12,12" offset="0,0" show-indices="false" expand-nested-arrays="false" xml:lang="de" />
    </resultFormat>
  </math>
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7. Verwenden Sie die Funktion det, um die Determinante der Matrix M zu ermitteln.

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Berechnen Sie alternativ die Determinante der Matrix M manuell.

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                    </id>
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                      <Span xml:lang="de" xmlns="http://schemas.microsoft.com/winfx/2006/xaml/presentation">c<Subscript xml:lang="de" xmlns="clr-namespace:Ptc.Wpf;assembly=Ptc.Core">1</Subscript></Span>
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              </id>
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                      <Span xml:lang="de" xmlns="http://schemas.microsoft.com/winfx/2006/xaml/presentation">b<Subscript xml:lang="de" xmlns="clr-namespace:Ptc.Wpf;assembly=Ptc.Core">0</Subscript></Span>
                    </id>
                    <id labels="VARIABLE" xml:space="preserve" xml:lang="de" label-is-contextual="true">
                      <Span xml:lang="de" xmlns="http://schemas.microsoft.com/winfx/2006/xaml/presentation">c<Subscript xml:lang="de" xmlns="clr-namespace:Ptc.Wpf;assembly=Ptc.Core">2</Subscript></Span>
                    </id>
                  </apply>
                  <apply xml:lang="de">
                    <mult xml:lang="de" />
                    <id labels="VARIABLE" xml:space="preserve" xml:lang="de" label-is-contextual="true">
                      <Span xml:lang="de" xmlns="http://schemas.microsoft.com/winfx/2006/xaml/presentation">b<Subscript xml:lang="de" xmlns="clr-namespace:Ptc.Wpf;assembly=Ptc.Core">2</Subscript></Span>
                    </id>
                    <id labels="VARIABLE" xml:space="preserve" xml:lang="de" label-is-contextual="true">
                      <Span xml:lang="de" xmlns="http://schemas.microsoft.com/winfx/2006/xaml/presentation">c<Subscript xml:lang="de" xmlns="clr-namespace:Ptc.Wpf;assembly=Ptc.Core">0</Subscript></Span>
                    </id>
                  </apply>
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              </parens>
            </apply>
          </apply>
          <apply xml:lang="de">
            <mult xml:lang="de" />
            <id labels="VARIABLE" xml:space="preserve" xml:lang="de" label-is-contextual="true">
              <Span xml:lang="de" xmlns="http://schemas.microsoft.com/winfx/2006/xaml/presentation">a<Subscript xml:lang="de" xmlns="clr-namespace:Ptc.Wpf;assembly=Ptc.Core">2</Subscript></Span>
            </id>
            <parens xml:lang="de">
              <apply xml:lang="de">
                <minus xml:lang="de" />
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                  </id>
                  <id labels="VARIABLE" xml:space="preserve" xml:lang="de" label-is-contextual="true">
                    <Span xml:lang="de" xmlns="http://schemas.microsoft.com/winfx/2006/xaml/presentation">c<Subscript xml:lang="de" xmlns="clr-namespace:Ptc.Wpf;assembly=Ptc.Core">1</Subscript></Span>
                  </id>
                </apply>
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8. Verwenden Sie die Funktion norm, um die Norm eines Vektors zu ermitteln, der die Elemente der Spalte 0 der Matrix M enthält.

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          <placeholder xml:lang="de" />
        </unitOverride>
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    </define>
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Berechnen Sie alternativ die Norm des Vektors v manuell.

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                </id>
                <real xml:lang="de">2</real>
              </apply>
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              <pow xml:lang="de" />
              <id labels="VARIABLE" xml:space="preserve" xml:lang="de" label-is-contextual="true">
                <Span xml:lang="de" xmlns="http://schemas.microsoft.com/winfx/2006/xaml/presentation">c<Subscript xml:lang="de" xmlns="clr-namespace:Ptc.Wpf;assembly=Ptc.Core">0</Subscript></Span>
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          <placeholder xml:lang="de" />
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    </define>
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      <matrix size="12,12" offset="0,0" show-indices="false" expand-nested-arrays="false" xml:lang="de" />
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