Linear representations and linear dimension reduction techniques are very common in signal and image processing. Many such applications reduce to solving problems of stochastic optimizations or statistical inferences on the set of all subspaces, i.e. a Grassmann manifold. Central to solving them is the computation of an “exponential” map (for constructing geodesics) and its inverse on a Grassma...

In this paper, we investigate the entanglement of multi-partite Grassmannian coherent states (GCSs) described by Grassmann numbers for n > 2 degree of nilpotency. Choosing an appropriate weight function, we show that it is possible to construct some wellknown entangled pure states, consisting of GHZ, W, Bell, cluster type and bi-separable states, which are obtained by integrating over tensor pr...

a r t i c l e i n f o Most geometric computer vision problems involve orthogonality constraints. An important subclass of these problems is subspace estimation, which can be equivalently formulated into an optimization problem on Grassmann manifolds. In this paper, we propose to use the conjugate gradient algorithm on Grassmann man-ifolds for robust subspace estimation in conjunction with the r...

I discuss a simple numerical algorithm for direct evaluation of multiple Grassmann integrals. The approach is exact, suffers no fermion sign problems, and allows arbitrarily complicated interactions. Memory requirements grow exponentially with the interaction range and the transverse size of the system. Low dimensional systems with 1000 Grassmann variables can be evaluated on a workstation. The...