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In mathematics, the Stiefel manifold V < sub > k </ sub >( R < sup > n </ sup >) is the set of all orthonormal k-frames in R < sup > n </ sup >.
That is, it is the set of ordered k-tuples of orthonormal vectors in R < sup > n </ sup >.
It is named after Swiss mathematician Eduard Stiefel.
Likewise one can define the complex Stiefel manifold V < sub > k </ sub >( C < sup > n </ sup >) of orthonormal k-frames in C < sup > n </ sup > and the quaternionic Stiefel manifold V < sub > k </ sub >( H < sup > n </ sup >) of orthonormal k-frames in H < sup > n </ sup >.
More generally, the construction applies to any real, complex, or quaternionic inner product space.
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