-------------------------------------------------------------------------------
help for geneigen                         (StataList distribution 20 July 2001)
-------------------------------------------------------------------------------

Eigenvalues of a real general matrix

        geneigen matrixname


Description

geneigen calculates the eigenvalues of a square matrix. The eigenvalues of a
square symmetric matrix may be calculated by mat symeigen, but official Stata
cannot calculate the eigenvalues of a nonsymmetric matrix. geneigen executes
EISPACK code to calculate the eigenvalues' real part, imaginary part, and
modulus via the QR algorithm for real Hessenberg matrices, as described in
Press et al. (1992, Chapter 11).

The routine returns a N by 4 matrix r(eigen), containing, respectively, the
modulus, real part, imaginary part, and cumulated modulus. The eigenvalues are
sorted in order of ascending moduli.

If Stata considers a matrix to be symmetric, its own mat symeigen routine
should be used rather than this routine.

Examples

        . mat kk=(1,2,3\-6,-8,-14\122,345,678)

        . geneigen kk

        . return list


Acknowledgements

The routine makes use of Jeroen Weesie's qsortidx routine, part of his very
useful qsort package. Thanks to Paul McGale for noting an error
in the translation of the routine.


References

Press, William H., Teukolsky, Saul A., Vetterling, William T. and Brian P. Flan
> nery.
Numerical Recipes in C, Second Edition. Cambridge: Cambridge University Press, 
> 1992.

Author


Christopher F Baum, Boston College, USA, baum@bc.edu


Also see