scholarly journals Relative Gottlieb Groups of Embeddings between Complex Grassmannians

2021 ◽  
Vol 2021 ◽  
pp. 1-7
Author(s):  
J. B. Gatsinzi
Keyword(s):  
Grassmann Manifold ◽  
Linear Subspaces ◽  
Complex Grassmann Manifold

Let Gr k , n be the complex Grassmann manifold of k -linear subspaces in ℂ n . We compute rational relative Gottlieb groups of the embedding i : Gr k , n ⟶ Gr k , n + r and show that the G -sequence is exact if r ≥ k n − k .

Bayesian and geometric subspace tracking

2004 ◽  
Vol 36 (1) ◽  
pp. 43-56 ◽  
Author(s):  
Anuj Srivastava ◽  
Eric Klassen
Keyword(s):  
Process Simulation ◽  
Sequential Monte Carlo ◽  
Grassmann Manifold ◽  
Array Signal Processing ◽  
Time Varying ◽  
Subspace Tracking ◽  
Bayesian Inferences ◽  
Sequential Monte Carlo Method ◽  
Complex Grassmann Manifold ◽  
Simulation Results

We address the problem of tracking the time-varying linear subspaces (of a larger system) under a Bayesian framework. Variations in subspaces are treated as a piecewise-geodesic process on a complex Grassmann manifold and a Markov prior is imposed on it. This prior model, together with an observation model, gives rise to a hidden Markov model on a Grassmann manifold, and admits Bayesian inferences. A sequential Monte Carlo method is used for sampling from the time-varying posterior and the samples are used to estimate the underlying process. Simulation results are presented for principal subspace tracking in array signal processing.

scholarly journals On the complex Grassmann manifold

1989 ◽  
Vol 33 (1) ◽  
pp. 170-179 ◽  
Author(s):  
Ari Babakhanian ◽  
Heisuke Hironaka
Keyword(s):  
Grassmann Manifold ◽  
Complex Grassmann Manifold
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