For $n$-dimensional real number set $\mathbb{R}^n$, its $n-1$ dimensional subspaces are called hyperplanes. Are there special names for lower dimensional subspace of $\mathbb{R}^n$?
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"Subspace of dimension $k$" (where $k \leq n$) is quite specific. – avs Feb 02 '17 at 17:42
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I have heard the term "hyperplane" refer to any $m$-dimensional subspace of $\mathbb R^n$ for $m<n$. I'd go with avs's suggestion though. – Wojowu Feb 02 '17 at 17:44
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I seem to recall $k$-flats referring to $k$-dimensional (affine) subspaces, but evidently it's less common than I'd thought. – pjs36 Feb 02 '17 at 17:44
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@Wojowu I used to think that way, too. But I recently read that hyperplane was only for n-1 subspace. Thus the question. – Guangliang Feb 02 '17 at 18:46
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An $n-k$ dimensional linear subspace of $\mathbb{R}^n$ is often called a codimension $k$ subspace. I don't believe a more general term exists.
Elchanan Solomon
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I bet you already know that :
A subspace of dimension $1$ is called a line.
A subspace of dimension $2$ is called a plane.
A subspace of codimension $1$ is called an hyperplane (as you stated).
C. Falcon
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