Definition
Hyperplane through the origin
For a given, nonzero 
, 
is a hyperplane.
is called the normal of the hyperplane.
Every vector 
in 
is orthogonal to 
.
General hyperplane
For a given, nonzero 
and 
, 
. It can be obtained by shifting 
in the direction of 
until it goes through 
It can also be written as 
is a linear subspace of 
with dimension of n - 1, it is a "thin".
is a hyperplane but not a subspace unless c = 0.