Language Reference

EIGVAL Function

computes eigenvalues

EIGVAL( )

where is a square numeric matrix.

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

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

  
    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 as follows:

  
               VAL 
  
               75        100 
               75       -100 
               25          0
 

Notice that is not symmetric and that 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 as follows:

  
          A             2 rows      1 col     (numeric) 
  
                        33.401219 
                         0.5987805