範例：使用 genvals 與 genvecs 函數

函數 > 向量與矩陣 > 陣列特性 > 範例：使用 genvals 與 genvecs 函數

範例：使用 genvals 與 genvecs 函數

1. 定義兩個方形矩陣。

按一下以複製此運算式

<region id="ID0E63IMB" top="153.60000000000002" left="38.400000000000006" xml:lang="zh_TW" height="118.6" width="216.77333333333334" xmlns="http://schemas.mathsoft.com/worksheet50">
  <math resultRef="0" xml:lang="zh_TW">
    <define xml:lang="zh_TW" xmlns="http://schemas.mathsoft.com/math50">
      <id labels="VARIABLE" xml:space="preserve" xml:lang="zh_TW">M</id>
      <matrix rows="6" cols="6" xml:lang="zh_TW">
        <real xml:lang="zh_TW">7.5</real>
        <real xml:lang="zh_TW">5.5</real>
        <real xml:lang="zh_TW">7.5</real>
        <real xml:lang="zh_TW">5.5</real>
        <real xml:lang="zh_TW">5.5</real>
        <real xml:lang="zh_TW">5.5</real>
        <real xml:lang="zh_TW">12</real>
        <real xml:lang="zh_TW">8.5</real>
        <real xml:lang="zh_TW">12</real>
        <real xml:lang="zh_TW">8.5</real>
        <real xml:lang="zh_TW">9</real>
        <real xml:lang="zh_TW">8.5</real>
        <real xml:lang="zh_TW">5.5</real>
        <real xml:lang="zh_TW">4</real>
        <real xml:lang="zh_TW">5.5</real>
        <real xml:lang="zh_TW">4</real>
        <real xml:lang="zh_TW">4.5</real>
        <real xml:lang="zh_TW">3.5</real>
        <real xml:lang="zh_TW">5.5</real>
        <real xml:lang="zh_TW">7.5</real>
        <real xml:lang="zh_TW">7.5</real>
        <real xml:lang="zh_TW">4.5</real>
        <real xml:lang="zh_TW">5</real>
        <real xml:lang="zh_TW">7</real>
        <real xml:lang="zh_TW">8.5</real>
        <real xml:lang="zh_TW">12</real>
        <real xml:lang="zh_TW">12</real>
        <real xml:lang="zh_TW">7.5</real>
        <real xml:lang="zh_TW">8</real>
        <real xml:lang="zh_TW">11</real>
        <real xml:lang="zh_TW">4</real>
        <real xml:lang="zh_TW">5</real>
        <real xml:lang="zh_TW">5.5</real>
        <real xml:lang="zh_TW">4</real>
        <real xml:lang="zh_TW">4</real>
        <real xml:lang="zh_TW">4.5</real>
      </matrix>
    </define>
  </math>
</region>

按一下以複製此運算式

<region id="ID0ER4IMB" top="153.60000000000002" left="307.20000000000005" xml:lang="zh_TW" height="118.6" width="214.28" xmlns="http://schemas.mathsoft.com/worksheet50">
  <math resultRef="2" xml:lang="zh_TW">
    <define xml:lang="zh_TW" xmlns="http://schemas.mathsoft.com/math50">
      <id labels="VARIABLE" xml:space="preserve" xml:lang="zh_TW">N</id>
      <matrix rows="6" cols="6" xml:lang="zh_TW">
        <real xml:lang="zh_TW">9</real>
        <real xml:lang="zh_TW">5.5</real>
        <real xml:lang="zh_TW">7.5</real>
        <real xml:lang="zh_TW">5.5</real>
        <real xml:lang="zh_TW">9.5</real>
        <real xml:lang="zh_TW">3</real>
        <real xml:lang="zh_TW">13</real>
        <real xml:lang="zh_TW">9</real>
        <real xml:lang="zh_TW">12</real>
        <real xml:lang="zh_TW">8.5</real>
        <real xml:lang="zh_TW">3</real>
        <real xml:lang="zh_TW">4.5</real>
        <real xml:lang="zh_TW">6.5</real>
        <real xml:lang="zh_TW">4</real>
        <real xml:lang="zh_TW">6</real>
        <real xml:lang="zh_TW">6</real>
        <real xml:lang="zh_TW">4.5</real>
        <real xml:lang="zh_TW">3.5</real>
        <real xml:lang="zh_TW">6.5</real>
        <real xml:lang="zh_TW">7.5</real>
        <real xml:lang="zh_TW">7.5</real>
        <real xml:lang="zh_TW">5</real>
        <real xml:lang="zh_TW">3</real>
        <real xml:lang="zh_TW">7</real>
        <real xml:lang="zh_TW">9.5</real>
        <real xml:lang="zh_TW">10</real>
        <real xml:lang="zh_TW">12</real>
        <real xml:lang="zh_TW">7.5</real>
        <real xml:lang="zh_TW">2.5</real>
        <real xml:lang="zh_TW">11</real>
        <real xml:lang="zh_TW">5</real>
        <real xml:lang="zh_TW">5</real>
        <real xml:lang="zh_TW">5.5</real>
        <real xml:lang="zh_TW">4</real>
        <real xml:lang="zh_TW">4</real>
        <real xml:lang="zh_TW">5</real>
      </matrix>
    </define>
    <resultFormat xml:lang="zh_TW">
      <matrix size="12,12" offset="0,0" show-indices="false" expand-nested-arrays="false" xml:lang="zh_TW" />
    </resultFormat>
  </math>
</region>

2. 使用 eigenvals 計算上述矩陣的本徵值。

按一下以複製此運算式

按一下以複製此運算式

3. 使用 genvals 計算本徵值向量。

按一下以複製此運算式

genvals 函數會傳回計算之本徵值的向量 vi，每一個值皆滿足其相關本徵向量 xi 的廣義本徵值問題 M · x = vi · N · x。

4. 將最後一個參數設為 L 再呼叫 genvecs，表示會計算左本徵向量。

按一下以複製此運算式

<region id="ID0EYGJMB" top="768.00000000000011" left="38.400000000000006" xml:lang="zh_TW" height="118.6" width="504.39333333333332" xmlns="http://schemas.mathsoft.com/worksheet50">
  <math resultRef="10" xml:lang="zh_TW">
    <eval xml:lang="zh_TW" xmlns="http://schemas.mathsoft.com/math50">
      <apply xml:lang="zh_TW">
        <id labels="FUNCTION" xml:space="preserve" xml:lang="zh_TW">genvecs</id>
        <sequence xml:lang="zh_TW">
          <id labels="VARIABLE" xml:space="preserve" xml:lang="zh_TW" label-is-contextual="true">M</id>
          <id labels="VARIABLE" xml:space="preserve" xml:lang="zh_TW" label-is-contextual="true">N</id>
          <str xml:space="preserve" xml:lang="zh_TW">L</str>
        </sequence>
      </apply>
      <unitOverride xml:lang="zh_TW">
        <placeholder xml:lang="zh_TW" />
      </unitOverride>
    </eval>
    <resultFormat xml:lang="zh_TW">
      <matrix size="12,12" offset="0,0" show-indices="false" expand-nested-arrays="false" xml:lang="zh_TW" />
    </resultFormat>
  </math>
</region>

genvecs 函數會傳回含有常態化左本徵向量的矩陣，此本徵向量會對應至 genvals 傳回之向量中，由上一個步驟所產生的本徴值。