The right eigenvector
, and the left eigenvector
, corresponding to an eigenvalue
, are defined by:
The eigenvectors are computed by inverse iteration. They are scaled so that
.
If
has been formed by reduction of a complex general matrix
to upper Hessenberg form, then the eigenvectors of
may be transformed to eigenvectors of
by a call to
f08nuf.
Each computed right eigenvector
is the exact eigenvector of a nearby matrix
, such that
. Hence the residual is small:
However, eigenvectors corresponding to close or coincident eigenvalues may not accurately span the relevant subspaces.
Similar remarks apply to computed left eigenvectors.
Please consult the
X06 Chapter Introduction for information on how to control and interrogate the OpenMP environment used within this routine. Please also consult the
Users' Note for your implementation for any additional implementation-specific information.
The real analogue of this routine is
f08pkf.