In geometry, a hyperplane is a generalisation of a normal two-dimensional plane in three-dimensional space to its (n − 1)-dimensional analogue in n-dimensional space, where n is an arbitrary number. Specifically, it is an affine subspace of codimension 1. It can be described by a linear equation of the following form:-
- a1x1 + a2x2 + ... + anxn = b
A zero-dimensional hyperplane is a point; a one-dimensional hyperplane is a (straight) line; and a two-dimensional hyperplane is a plane. The term realm has been advocated for a three-dimensional hyperplane, but this is not in common use.
A hyperplane is not to be confused with a hypersonic aircraft.