In geometry, as a plane has one less dimension than space, a hyperplane is a subspace of one dimension less than its ambient space. A hyperplane of an n-dimensional space is a flat subset with dimension n − 1. By its nature, it separates the space into two half spaces. == Technical description == In geometry, a hyperplane of an n-dimensional spa...
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http://en.wikipedia.org/wiki/Hyperplane
An affine set of dimension (n-1): {x: a'x = b}, where a is a nonzero vector, called the normal of the hyperplane.
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http://glossary.computing.society.informs.org/index.php?page=H.html
noun An infinite set of points extending into n dimensions. A one dimensional hyperplane is a line, two-dimensional is a plane, three dimensional is a realm, and four-dimensional is a flune. A hyperplane of n dimensions intersects a plane of n+1 dimensions into two parts. See the chart under tetraspace.
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a subspace of a vector space that has dimension one less than the dimension of the vector space.
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https://www.infoplease.com/dictionary/hyperplane
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