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In mathematics, the Stiefel manifold is the set of all orthonormal k-frames in That is, it is the set of ordered orthonormal k-tuples of vectors in It is named after Swiss mathematician Eduard Stiefel. Likewise one can define the complex Stiefel manifold of orthonormal k-frames in and the quaternionic Stiefel manifold of orthonormal k-frames in . More generally, the construction applies to any real, complex, or quaternionic inner product space.

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  • Stiefel-Mannigfaltigkeit
  • Stiefel manifold
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  • In der Mathematik parametrisieren Stiefel-Mannigfaltigkeiten, benannt nach Eduard Stiefel, die Orthonormalbasen der Unterräume eines Vektorraumes.
  • In mathematics, the Stiefel manifold is the set of all orthonormal k-frames in That is, it is the set of ordered orthonormal k-tuples of vectors in It is named after Swiss mathematician Eduard Stiefel. Likewise one can define the complex Stiefel manifold of orthonormal k-frames in and the quaternionic Stiefel manifold of orthonormal k-frames in . More generally, the construction applies to any real, complex, or quaternionic inner product space.
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  • Stiefel_manifold
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  • Stiefel manifold
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  • In der Mathematik parametrisieren Stiefel-Mannigfaltigkeiten, benannt nach Eduard Stiefel, die Orthonormalbasen der Unterräume eines Vektorraumes.
  • In mathematics, the Stiefel manifold is the set of all orthonormal k-frames in That is, it is the set of ordered orthonormal k-tuples of vectors in It is named after Swiss mathematician Eduard Stiefel. Likewise one can define the complex Stiefel manifold of orthonormal k-frames in and the quaternionic Stiefel manifold of orthonormal k-frames in . More generally, the construction applies to any real, complex, or quaternionic inner product space. In some contexts, a non-compact Stiefel manifold is defined as the set of all linearly independent k-frames in or this is homotopy equivalent, as the compact Stiefel manifold is a deformation retract of the non-compact one, by Gram–Schmidt. Statements about the non-compact form correspond to those for the compact form, replacing the orthogonal group (or unitary or symplectic group) with the general linear group.
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