A generalization of classical theorems on the existence of sections of real, complex and quaternionic Stiefel manifolds over spheres is proved. We obtain a complete list of Lie group homomorphisms ρ : G → Gn, where Gn is one of the groups SO(n), SU(n), Sp(n) and G is one of the groups SO(k), SU(k), Sp(k), which reduce the structure group Gn in the fibre bundle Gn → Gn+1 → Gn+1/Gn.

In this paper we consider a Procrustes problem on the set of sub-Stiefel matrices. A sub-Stiefel matrix is a matrix that results from deleting simultaneously the last row and the last column of an orthogonal matrix. An iterative algorithm for computing the solution of the sub-Stiefel Procrustes problem is proposed. For these purposes we investigate the properties of sub-Stiefel matrices. We als...

A low complexity Lie group method for numerical integration of ordinary differential equations on the orthogonal Stiefel manifold is presented. Based on the quotient space representation of the Stiefel manifold we provide a representation of the tangent space suitable for Lie group methods. According to this representation a special type of generalized polar coordinates (GPC) is defined and use...

Optimization on Stiefel manifolds was discussed by Rapcsák in earlier papers. There, some numerical methods of global optimization are dealt with and tested on Stiefel manifolds. In the paper the structure of the optimizer points is given in some particular problem instances and for a special form of a quadratic problem defined on a Stiefel manifold. Some reduction tricks and results are obtain...

In this note, we characterize the convex hull of the Stiefel manifold and we find its strong convexity parameter. We also introduce the notion of roundness of a set and show that the Stiefel manifold is round.

Applications of multiple input and multiple output (MIMO) with Stiefel manifold are growing in the next generation communications and their system engineering developments. These applications need to be optimized efficiently with less complexity and cost. In this research, optimization problems in MIMO systems using Stiefel manifold are considered. As far as general manifolds are concerned, opt...

Optimization on Stiefel manifolds was discussed by Rapcsák in earlier papers, and some global optimization methods were considered and tested on Stiefel manifolds. In the paper, test functions are given with known global optimum points and their optimal function values. A restriction, which leads to a discretization of the problem is suggested, which results in a problem equivalent to the well-...

In their paper on discrete analogues of some classical systems such as the rigid body and the geodesic flow on an ellipsoid, Moser and Veselov introduced their analysis in the general context of flows on Stiefel manifolds. We consider here a general class of continuous time, quadratic cost, optimal control problems on Stiefel manifolds, which in the extreme dimensions again yield these classica...

With methods from Riemannian geometry bounds for the minimal distance of packings in the Graßmann and Stiefel manifolds will be derived and analysed, revealing implications for certain aspects of coding theory. Though motivated from coding theory on the Graßmann and Stiefel manifolds, the method can be generalised to arbitrary Riemannian homogeneous spaces as well.