Originally motivated by diffractive optics,
various matrix factorization problems are under study. Further investigation
have give rise to a link between matrix analysis and computations with classical
topics in algebraic geometry. For instance, we have a natural concept for the spectrum
of a matrix subspace given in terms determinantal hypersurfaces in the complex projective space. Aside from fundamental concepts, these ideas are also being planned
to be used in preconditioning large linear systems.