Esempio: ricerca degli autovettori sinistro e destro

Funzioni > Vettore e matrice > Caratteristiche degli array > Esempio: ricerca degli autovettori sinistro e destro

Per evitare corrispondenze errate a livello logico quando si eseguono confronti booleani, attivare l'opzione Uguaglianza approssimativa nell'elenco a discesa Opzioni calcolo.

1. Definire una matrice reale quadrata.

2. Utilizzare la definizione di base di eigenval per trovare le espressioni lambda della matrice A.

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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. In alternativa, utilizzare la funzione eigenvals per trovare le espressioni lambda della matrice A.

Ricerca degli autovettori destri

1. Utilizzare la funzione eigenvecs per trovare gli autovettori destri (default) della matrice A.

2. Mostrare che la relazione A x Rn = λn x Rn è true.

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Le relazioni sono true.

Ricerca degli autovettori sinistri

1. Utilizzare la funzione eigenvecs per trovare gli autovettori sinistri della matrice A.

2. Mostrare che la relazione LnT x A = λn x LnT è true.

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La relazione è true.

Argomenti correlati

Autovettori e autovalori

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