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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 0Notice 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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