```! Compute eigenvalues and eigenvectors; ! Keywords: Eigenvalue, Eigenvector, Matt Damon, PCA, Population growth, Principal Component Analysis, Good Will Hunting; SETS: item: evalr, evali; ixi( item, item): a, evecr, eveci; ENDSETS DATA: ! Case: Finding the eigenvalues of these two matrices was listed as an exercise on the board to be solved by Matt Damon in the movie "Good Will Hunting"; ! item = 1..3; ! A = 1 1 0 1 1 -2 2 1 0; ! A = 2 -1 -1 -1 2 -1 -1 -1 2; ! A Covariance matrix; ! item = ATT GMC USX; ! A = .01080754 .01240721 .01307513 .01240721 .05839170 .05542639 .01307513 .05542639 .09422681; ! A population change matrix; item = Bunnies Clover Foxes; A = 0.612 2.291 -1.200 -0.295 2.321 -0.560 0.500 -0.050 0.110 ; ENDDATA CALC: ! Get the eigenvalues(real part), eigenvectors(real part), eigenvalues(imaginary part), and eigenvectors(imaginary part); evalr, evecr, evali, eveci = @eigen(a); ENDCALC DATA: @TEXT() = ''; @TEXT() = 'eigenvalues, real part:'; @TEXT() = @table( evalr); @TEXT() = ''; @TEXT() = 'eigenvectors(columns), real part:'; @TEXT() = @table( evecr); @TEXT() = ''; @TEXT() = 'eigenvalues, imaginary part:'; @TEXT() = @table( evali); @TEXT() = ''; @TEXT() = 'eigenvectors(columns), imaginary part:'; @TEXT() = @table( eveci); ENDDATA ```