text: Any hyperplane of a Euclidean space has exactly two unit normal vectors: . In particular, if we consider  equipped with the conventional inner product (dot product), then one can define the affine subspace with normal vector  and origin translation  as the set of all  such that .
  Affine hyperplanes are used to define decision boundaries in many machine learning algorithms such as linear-combination (oblique) decision trees, and perceptrons.
  Vector hyperplanes
  In a vector space, a vector hyperplane is a subspace of codimension 1, only possibly shifted from the origin by a vector, in which case it is referred to as a flat. Such a hyperplane is the solution of a single linear equation.
  Projective hyperplanes
  Projective hyperplanes, are used in projective geometry.  A projective subspace is a set of points with the property that for any two points of the set, all the points on the line determined by the two points are contained in the set. Projective geometry can be viewed as affine geometry with vanishing points (points at infinity) added.  An affine hyperplane together with the associated points at infinity forms a projective hyperplane.  One special case of a projective hyperplane is the infinite or ideal hyperplane, which is defined with the set of all points at infinity.