k - flats

Let  
\[\mathbb{R}^n\]
  be the set of n - tuples. A k - flat  
\[F\]
, or linear variety or affine subspace, in  
\[\mathbb{R}^n\]
  is the set of all n - tuples of the form  
\[P+V\]
, where  
\[P\]
  is the position vector of a point of  
\[\mathbb{R}^n\]
  and  
\[\mathbf{w}\]
  is from a a k - dimensional subspace of  
\[\mathbb{R}^n\]
.
\[W\]
  is called a direction space of  
\[F\]
  and we can write  
\[F=P+W\]
.
A point is a 0 - flat (ha dimension 0).
A line is a 1 - flat (ha dimension 1).
A plane is a 2 - flat (ha dimension 2).

You have no rights to post comments