TITLE(eigen @@ Spectral Decomposition of a Matrix)
USAGE(
eigen(x, symmetric=all(x==t(x)), only.values=FALSE)
eigen.rs(x, only.values=FALSE)
eigen.rg(x, only.values=FALSE)
)
ALIAS(eigen)
ALIAS(eigen.rs)
ALIAS(eigen.rg)
ARGUMENTS(
ARG(x @@ a matrix whose spectral decomposition is to be computed.)
ARG(symmetric @@ if LANG(TRUE), the matrix is assumed to be symmetric and
only its lower triangle is used.)
ARG(only.values @@ if LANG(TRUE), only the eigenvalues are computed
and returned, otherwise both eigenvalues and eigenvectors are
returned.)
)
DESCRIPTION(
These functions provide an interface to the EISPACK routines
LANG(RS) and LANG(RG).
The functions LANG(eigen.rs) and LANG(eigen.rg) provide
versions of the decomposition for the symmetric and
general cases.
They provide a slight performance advantage by skipping
the symmetry test of LANG(eigen).
)
VALUE(
The spectral decomposition of LANG(x) is returned
as components of a list.
If the eigenvalues are all real the list contains components;
LANG(values), a vector containing the eigenvalues of LANG(x) and
LANG(vectors), a matrix whose columns contain the eigenvectors of LANG(x).
PARA
If some of the eigenvalues are complex, the list contains additional components;
LANG(values.im) and LANG(vectors.im), which respectively contain
the imaginary parts of the eigenvalues and eigenvectors of LANG(x).
)
REFERENCES(
Smith, B. T, J. M. Boyle, J. J. Dongarra, B. S. Garbow, Y. Ikebe,
V. Klema, C. B. Moler (1976).
ITALIC(Matrix Eigensystems Routines - EISPACK Guide).
Springer-Verlag Lecture Notes in Computer Science.
)
SEEALSO(
LANG(LINK(svd)), LANG(LINK(qr)).
)
