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Toolbox for grassmann manifold computations
, 2008
"... This a description and user guide for an object oriented toolbox written in matlab for computations defined on Grassmann manifolds and products of Grassmann manifolds. It implements basic operations as geodesic movement and parallel transport of tangent vectors. 1 Content of toolbox There are two cl ..."
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This a description and user guide for an object oriented toolbox written in matlab for computations defined on Grassmann manifolds and products of Grassmann manifolds. It implements basic operations as geodesic movement and parallel transport of tangent vectors. 1 Content of toolbox There are two
The Geometry and Topology on Grassmann Manifolds
, 2006
"... This paper shows that the Grassmann Manifolds GF(n,N) can all be imbedded in an Euclidean space MF(N) naturally and the imbedding can be realized by the eigenfunctions of Laplacian △ on GF(n,N). They are all minimal submanifolds in some spheres of MF(N) respectively. Using these imbeddings, we const ..."
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This paper shows that the Grassmann Manifolds GF(n,N) can all be imbedded in an Euclidean space MF(N) naturally and the imbedding can be realized by the eigenfunctions of Laplacian △ on GF(n,N). They are all minimal submanifolds in some spheres of MF(N) respectively. Using these imbeddings, we
Metric Entropy of the Grassmann Manifold
"... Abstract. The knowledge of the metric entropy of precompact subsets of operators on finite dimensional Euclidean space is important in particular in the probabilistic methods developped by E. D. Gluskin and S. Szarek for constructing certain random Banach spaces. We give a new argument for estimatin ..."
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Cited by 4 (0 self)
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for estimating the metric entropy of some subsets such as the Grassmann manifold equipped with natural metrics. Here, the Grassmann manifold is thought of as the set of orthogonal projection of given rank.
Packings on the Grassmann Manifold
"... Abstract — We show that orthogonal spacetime block codes may be identified with packings on the Grassmann manifold. We describe a general criterion for packings on the Grassmann manifold that yield coherent spacetime constellations with the same code properties that make orthogonal spacetime bloc ..."
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Abstract — We show that orthogonal spacetime block codes may be identified with packings on the Grassmann manifold. We describe a general criterion for packings on the Grassmann manifold that yield coherent spacetime constellations with the same code properties that make orthogonal space
LANCZOS ALGORITHM ON THE GRASSMANN MANIFOLD
, 2008
"... The problem of computing eigenvalues, eigenvectors and invariant subspaces is always present in areas as diverse as Engineering, Physics, Computer Science and Mathematics. Considering the importance of these problems in many practical applications, it is not surprising that has been and continues to ..."
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to be the subject of intense research. We developed a new Lanczos algorithm on the Grassmann manifold. This work comes in the wake of the article by A. Edelman, T. A. Arias and S. T. Smith, The geometry of algorithms with orthogonality constraints, where they presented a new conjugate gradient algorithm
Efficient Algorithms For Inferences On Grassmann Manifolds
 IN PROCEEDINGS OF 12 TH IEEE WORKSHOP ON STATISTICAL SIGNAL PROCESSING
, 2003
"... 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 ..."
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Cited by 32 (4 self)
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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
Bounds on packings of spheres in the Grassmann manifolds
, 2000
"... We derive the VarshamovGilbert and Hamming bounds for packings of spheres (codes) in the Grassmann manifolds over $\mathbb R$ and $\mathbb C$. The distance between two $k$planes is defined as $\rho(p,q)=(\sin^2\theta_1 \dots \sin^2\theta_k)^{1/2}$, where $\theta_i, 1\le i\le k$, are the principal ..."
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Cited by 42 (1 self)
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We derive the VarshamovGilbert and Hamming bounds for packings of spheres (codes) in the Grassmann manifolds over $\mathbb R$ and $\mathbb C$. The distance between two $k$planes is defined as $\rho(p,q)=(\sin^2\theta_1 \dots \sin^2\theta_k)^{1/2}$, where $\theta_i, 1\le i\le k
Results 1  10
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7,180