例:左と右の固有ベクトルを求める

関数 > ベクトルと行列 > 配列の特徴 > 例:左と右の固有ベクトルを求める

例:左と右の固有ベクトルを求める

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1. 正方実数行列を定義します。

2. eigenval の基本定義を使用して、行列 A のラムダを求めます。

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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. または、関数eigenvalsを使用して行列 A のラムダを求めます。

右の固有ベクトルを求める

1. 関数eigenvecsを使用して、行列 A の右 (デフォルト) の固有ベクトルを求めます。

2. 関係 A x Rn = λn x Rn が真であることを示します。

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関係は真です。

左の固有ベクトルを求める

1. 関数 eigenvecs を使用して行列 A の左の固有ベクトルを求めます。

2. 関係 LnT x A = λn x LnT が真であることを示します。

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関係は真です。