hyperplane

In geometry, a hyperplane is a linear, affine, or projective subspace of codimension 1. In particular, in a three-dimensional space, a hyperplane is the usual plane. In a two-dimensional space, a hyperplane is a line. In a one-dimensional space, a hyperplane is a point. An affine hyperplane can be described by a non-degenerate linear equation of the following form:

a₁x₁ + a₂x₂ + ... + a_nx_n = b.

A linear hyperplane is similar but with b = 0. See also hypersurface.

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.

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