Rational Canonical Form

Infinite-dimensional versions of the primary, cyclic and Jordan decompositions

The famous primary and cyclic decomposition theorems along with the tightly related rational and Jordan canonical forms are extended to linear spaces of infinite dimensions with counterexamples showing the scope of extensions.

Determining the order of minimal realization of descriptor systems without use of the Weierstrass canonical form

A common method to determine the order of minimal realization of a continuous linear time invariant descriptor system is to decompose it into slow and fast subsystems using the Weierstrass canonical form. The Weierstrass decomposition should be avoided because it is generally an ill-conditioned problem that requires many complex calculations especially for high-dimensional systems. The present ...

A Rational Canonical Form Algorithm

Symmetries of canal surfaces and Dupin cyclides

We develop a characterization for the existence of symmetries of canal surfaces defined by a rational spine curve and rational radius function. In turn, this characterization inspires an algorithm for computing the symmetries of such canal surfaces. For Dupin cyclides in canonical form, we apply the characterization to derive an intrinsic description of their symmetries and symmetry groups, whi...

Towards Generalizing Schubert Calculus in the Symplectic Category

The main purpose of this article is to extend some of the ideas from Schubert calculus to the more general setting of Hamiltonian torus actions on compact symplectic manifolds with isolated fixed points. Given a generic component Ψ of the moment map, which is a Morse function, we define a canonical class αp in the equivariant cohomology of the manifold M for each fixed point p ∈ M. When they ex...