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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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