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gptkbp:instanceOf
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gptkb:mathematical_concept
gptkb:Riemannian_manifold
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gptkbp:category
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gptkb:topology
gptkb:Riemannian_manifold
homogeneous space
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gptkbp:compact
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true
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gptkbp:complexVersion
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gptkb:complex_Stiefel_manifold
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gptkbp:defines
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the set of all orthonormal k-frames in n-dimensional Euclidean space
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gptkbp:dimensions
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nk - k(k+1)/2
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gptkbp:field
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gptkb:mathematics
differential geometry
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gptkbp:generalizes
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orthogonal group
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gptkbp:hasSpecialCase
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gptkb:Grassmannian_(when_k=n)
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gptkbp:homogeneousSpaceOf
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gptkb:orthogonal_group_O(n)
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https://www.w3.org/2000/01/rdf-schema#label
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Stiefel manifold
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gptkbp:introducedIn
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1935
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gptkbp:isQuotientOf
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O(n)/O(n-k)
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gptkbp:namedAfter
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gptkb:Eduard_Stiefel
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gptkbp:notation
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V_k( 53c^n)
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gptkbp:realVersion
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gptkb:real_Stiefel_manifold
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gptkbp:relatedTo
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gptkb:Lie_group
Grassmannian
orthogonal group
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gptkbp:symplecticVersion
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gptkb:symplectic_Stiefel_manifold
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gptkbp:usedIn
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gptkb:machine_learning
gptkb:signal_processing
computer vision
statistics
optimization
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gptkbp:bfsParent
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gptkb:Grassmannian
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gptkbp:bfsLayer
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5
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