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 $\mathbb{R}^n$?
Are there special names for lower dimensional subspace of $\mathbb{R}^n$
0
$\begingroup$
real-numbers
-
0"Subspace of dimension $k$" (where $k \leq n$) is quite specific. – 2017-02-02
-
0I have heard the term "hyperplane" refer to any $m$-dimensional subspace of $\mathbb R^n$ for $m
-
0I seem to recall *$k$-flats* referring to $k$-dimensional (affine) subspaces, but evidently it's less common than I'd thought. – 2017-02-02
-
0@Wojowu I used to think that way, too. But I recently read that hyperplane was only for n-1 subspace. Thus the question. – 2017-02-02
2 Answers
1
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.
1
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).