Editing Hyperplane (section)

== Technical description ==
In [[geometry]], a '''hyperplane''' of an [[n-dimensional space|''n''-dimensional space]] ''V'' is a subspace of dimension ''n''&nbsp;&minus;&nbsp;1, or equivalently, of [[codimension]]&nbsp;1 in&nbsp;''V''. The space ''V'' may be a [[Euclidean space]] or more generally an [[affine space]], or a [[vector space]] or a [[projective space]], and the notion of hyperplane varies correspondingly since the definition of subspace differs in these settings; in all cases however, any hyperplane can be given in [[coordinate]]s as the solution of a single (due to the "codimension&nbsp;1" constraint) [[algebraic equation]] of degree&nbsp;1.

If ''V'' is a vector space, one distinguishes "vector hyperplanes" (which are [[linear subspace]]s, and therefore must pass through the origin) and "affine hyperplanes" (which need not pass through the origin; they can be obtained by [[translation (geometry)|translation]] of a vector hyperplane). A hyperplane in a Euclidean space separates that space into two [[Half-space (geometry)|half space]]s, and defines a [[reflection (mathematics)|reflection]] that fixes the hyperplane and interchanges those two half spaces.