Let , , ..., be scalars not all equal to 0. Then the set consisting of all vectors
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.