In §9.4 the scope of the algebraic eigenvalue problem is
widened to geometrical properties of invariant subspaces. A template is
presented that can be used to solve variational problems that are defined
over sets of subspaces. More specifically, algorithms and software are provided
for the optimization of a real valued function over
such that
.
It is shown, by example, how many eigenvalue-related problems,
such as the Procrustes problem, determination of nearest Jordan structure,
and trace minimization, can be attacked with the given techniques.