We study the problem of feedback control for skew-symmetric and skewHamiltonian transfer functions using skew-symmetric controllers. This extends work of Helmke, et al., who studied static symmetric feedback control of symmetric and Hamiltonian linear systems. We identify spaces of linear systems with symmetry as natural subvarieties of the moduli space of rational curves in a Grassmannian, giv...

An operator T on a complex Hilbert space H is called skew symmetric if T can be represented as a skew symmetric matrix relative to some orthonormal basis for H. In this note, we explore the structure of skew symmetric operators with disconnected spectra. Using the classical Riesz decomposition theorem, we give a decomposition of certain skew symmetric operators with disconnected spectra. Severa...

Unitary symmetric completions of complex symmetric matrices are obtained via Autonne decomposition. The problem arises from atomic physics. Of independent interest unitary skew symmetric completions of skew symmetric matrices are also obtained by Hua decomposition.

We introduce the maximumskew-symmetric ow problem which generalizes ow and matching problems. We develop a theory of skew-symmetric ows that is parallel to the classical ow theory. We use the newly developed theory to extend, in a natural way, the blocking ow method of Dinitz to the skew-symmetric ow case. In the special case of the skew-symmetric ow problem that corresponds to cardinality matc...