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## Main Question or Discussion Point

If X is a Euclidean subspace, what does Fr(X) mean? I have been unable to find any references to this notation, so any help would be appreciated.

- Thread starter SirJay
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If X is a Euclidean subspace, what does Fr(X) mean? I have been unable to find any references to this notation, so any help would be appreciated.

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fzero

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1. A frame of X viewed as a vector space. If X is embedded in another vector space V, then the a basis on V, restricted to X, would be naturally viewed as a collection of linearly dependent vectors that span X.

2. Fr(X) could be a space defined in a similar way to the Grassmannian; perhaps as the space of all copies of X in the original space.

3. With X viewed as a vector space that is a subspace of a manifold M, we might imagine using X to construct a vector bundle over M. If the notation is abused to also call this bundle X, then Fr(X) could be the frame bundle associated to this vector bundle.

I'm sure there are less obvious possibilities. It could even be that the context is Frechet spaces or manifolds.

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