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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 + ... + anxn = 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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