MAT #EIGEN(A,D)
computes eigenvalues D
of an n*n nonsymmetric matrix A.
MAT #EIGEN(A,D,R)
computes eigenvalues D and (right) eigenvectors R
MAT #EIGEN(A,D,R,L)
computes also left eigenvectors L.
D will be an n*n tridiagonal matrix where real eigenvalues
occupy diagonal elements while the real and imaginary parts of
pairs of complex eigenvalues u+iv, u-iv occupy respectively
the diagonal and off-diagonal corners of 2*2 blocks.
Afterwards an n*2 matrix D2 of real and imaginary parts of eigenvalues
can be created by
MAT #EIGEN #VAL D,D2 .
Matrices A,D,R,L satisfy, for example, the equations
A=RDL, AR=RD, LA=DL.
The algorithm of MAT #EIGEN is based on a norm reducing Jacobi type method
presented by P.J.Eberlein and J.Boothroyd in Handbook for Automatic
Computation, Vol.2 (Wilkinson and Reinsch, Springer 1971, pp.327-338).
The original algorithm has been speeded up by a factor ca. 7 by SM (1998).
For a n*n symmetric matrix A it is absolutely more efficient to use
MAT SPECTRAL DECOMPOSITION OF A TO R,D
for example.
A = More about additional MAT #operations
M = More about MAT operations
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