Example: Using genvals and genvecs Functions

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Example: Using genvals and genvecs Functions

1. Define two square matrices.

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  <math resultRef="6">
    <define xmlns="http://schemas.mathsoft.com/math50">
      <id labels="VARIABLE" xml:space="preserve">M</id>
      <matrix rows="6" cols="6">
        <real>7.5</real>
        <real>5.5</real>
        <real>7.5</real>
        <real>5.5</real>
        <real>5.5</real>
        <real>5.5</real>
        <real>12</real>
        <real>8.5</real>
        <real>12</real>
        <real>8.5</real>
        <real>9</real>
        <real>8.5</real>
        <real>5.5</real>
        <real>4</real>
        <real>5.5</real>
        <real>4</real>
        <real>4.5</real>
        <real>3.5</real>
        <real>5.5</real>
        <real>7.5</real>
        <real>7.5</real>
        <real>4.5</real>
        <real>5</real>
        <real>7</real>
        <real>8.5</real>
        <real>12</real>
        <real>12</real>
        <real>7.5</real>
        <real>8</real>
        <real>11</real>
        <real>4</real>
        <real>5</real>
        <real>5.5</real>
        <real>4</real>
        <real>4</real>
        <real>4.5</real>
      </matrix>
    </define>
    <resultFormat>
      <matrix size="12,12" offset="0,0" show-indices="false" expand-nested-arrays="false" />
    </resultFormat>
  </math>
</region>

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

2. Use eigenvals to calculate the eigenvalues of the above matrices.

3. Use genvals to compute a vector of eigenvalues.

The genvals function returns a vector of computed eigenvalues, vi, each of which satisfies the generalized eigenvalue problem M · x = vi · N · x for its associated eigenvector xi.

4. Call genvecs with the last parameter set to L, meaning that left eigenvectors are calculated.

The genvecs function returns a matrix containing the normalized left eigenvectors corresponding to the eigenvalues in the vector returned by genvals that was generated in the previous step.

Related Topics

Eigenvectors and Eigenvalues

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