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.

Susan Blackford 2000-11-20