Beispiel: Linken und rechten Eigenvektor ermitteln

Funktionen > Vektor und Matrix > Array-Eigenschaften > Beispiel: Linken und rechten Eigenvektor ermitteln

Um logische Konflikte zu vermeiden, wenn Sie boolesche Vergleiche ausführen, aktivieren Sie Annähernde Gleichheit in der Dropdown-Liste Berechnungsoptionen.

1. Definieren Sie eine reelle, quadratische Matrix.

2. Verwenden Sie die grundlegende Definition von eigenval, um die Lambdas der Matrix A zu suchen.

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  <math resultRef="28">
    <symEval xmlns="http://schemas.mathsoft.com/math50">
      <apply>
        <absval />
        <apply>
          <minus />
          <id labels="VARIABLE" xml:space="preserve" label-is-contextual="true">A</id>
          <apply>
            <mult />
            <id xml:space="preserve">λ</id>
            <id labels="VARIABLE" xml:space="preserve" label-is-contextual="true">I</id>
          </apply>
        </apply>
      </apply>
      <command>
        <id xml:space="preserve">factor</id>
      </command>
      <symResult>
        <apply>
          <mult />
          <parens>
            <apply>
              <plus />
              <id labels="*" xml:space="preserve">λ</id>
              <real>3</real>
            </apply>
          </parens>
          <parens>
            <apply>
              <minus />
              <id labels="*" xml:space="preserve">λ</id>
              <real>4</real>
            </apply>
          </parens>
        </apply>
      </symResult>
    </symEval>
    <formattingOverride BackgroundColor="#00FFFFFF" />
  </math>
</region>

3. Stattdessen können Sie auch die Funktion eigenvals verwenden, um die Lambdas der Matrix A zu suchen.

Die rechten Eigenvektoren suchen

1. Verwenden Sie die Funktion eigenvecs, um die rechten (Standard)-Eigenvektoren der Matrix A zu suchen.

2. Zeigen Sie, dass die Beziehung A x Rn = λn x Rn wahr ist.

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Die Beziehungen sind wahr.

Die linken Eigenvektoren suchen

1. Verwenden Sie die Funktion eigenvecs, um die linken Eigenvektoren der Matrix A zu suchen.

2. Zeigen Sie, dass die Beziehung LnT x A = λn x LnT wahr ist.

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Die Beziehung ist wahr.

Zugehörige Themen

Eigenvektoren und Eigenwerte

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