EIGVAL Function

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EIGVAL Function

computes eigenvalues

EIGVAL( A)

where A is a square numeric matrix.

The EIGVAL function returns a column vector of the eigenvalues of A. See the description of the EIGEN subroutine for more details.

The following code computes Example 7.1.1 from Golub and Van Loan (1989):

   proc iml;

      a = {  67.00  177.60  -63.20 ,
            -20.40   95.88  -87.16 ,
             22.80   67.84   12.12 };

      val = EIGVAL(a);
      print val;

The matrix produced containing the eigenvalues is

              VAL

              75        100
              75       -100
              25          0

Notice that since a is not symmetric the eigenvalues are complex. The first column of the VAL matrix is the real part and the second column is the complex part of the three eigenvalues.

A symmetric example follows:

   x={1 1,1 2,1 3,1 4};
   xpx=t(x)*x;
   a=eigval(xpx);         /* xpx is a symmetric matrix */

The matrix produced containing the eigenvalues is

         A             2 rows      1 col     (numeric)

                       33.401219
                        0.5987805

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