Nonimmersion theorems for Grassmann manifolds

Grassmann Registration Manifolds for Face Recognition

Motivated by image perturbation and the geometry of manifolds, we present a novel method combining these two elements. First, we form a tangent space from a set of perturbed images and observe that the tangent space admits a vector space structure. Second, we embed the approximated tangent spaces on a Grassmann manifold and employ a chordal distance as the means for comparing subspaces. The mat...

Space Forms of Grassmann Manifolds

Efficient Algorithms for Inferences on Grassmann Manifolds

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...

The Capelli Identity for Grassmann Manifolds

The column space of a real n× k matrix x of rank k is a k-plane. Thus we get a map from the space X of such matrices to the Grassmannian G of k-planes in Rn, and hence a GLn-equivariant isomorphism C∞ (G) ≈ C∞ (X)k . We consider the On ×GLk-invariant differential operator C on X given by C = det ( xx ) det ( ∂∂ ) , where x = (xij) , ∂ = ( ∂ ∂xij ) . By the above isomorphism C defines an On-inva...

A Star Product for Complex Grassmann Manifolds

We explicitly construct a star product for the complex Grassmann manifolds using the method of phase space reduction. Functions on C(p+q)·p ∗, the space of (p + q)× p matrices of rank p, invariant under the right action of Gl(p, C) can be regarded as functions on the Grassmann manifold Gp,q(C), but do not form a subalgebra whereas functions only invariant under the unitary subgroup U(p) ⊂ Gl(p,...