Let 
, 
, ..., 
be scalars not all equal to 0.
Then the set 
consisting of all vectors
![X=[x_1; x_2; |; x_n]](/images/equations/Hyperplane/NumberedEquation1.svg) |
in 
such that
 |
for 
a constant is a subspace
of 
called a hyperplane.
More generally, a hyperplane is any codimension-1 vector subspace of a vector
space. Equivalently, a hyperplane 
in a vector space 
is any subspace such that 
is one-dimensional. Equivalently,
a hyperplane is the linear transformation
kernel of any nonzero linear map
from the vector space to the underlying field.
