# hyperplane

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## hyperplane

[¦hī·pər‚plān]
(mathematics)
A hyperplane is an (n- 1)-dimensional subspace of an n-dimensional vector space.
References in periodicals archive ?
the point of intersection of all the hyperplanes), then reflecting a point on the surface of the hypersphere about a hyperplane (by means of an orthogonal projection through the hyperplane), results in another point also on the surface of the hypersphere.
The hyperplane H separates the halfplane A, above, from the halfplane B, below.
At this point of tangency between the hyperplane and the ellipsoid, the outward normal of the ellipsoid is 2[[SIGMA].
If constant returns to scale prevails, the best fitting hyperplane will have U equal to zero.
Moreover, they introduced the beautiful idea of rounding a solution to this relaxation to a feasible cut with a random hyperplane through the origin.
For linear programming, the first operation can be performed in O(d) time, by substituting the coordinates of the vertex w(B) into the equation of the hyperplane defining h.
There are some shifts which, therefore, also change a country's terms of trade, but a country then finds itself on a new hyperplane which has the same stability properties as the old one.
Once in a long while, a randomly selected point can land close to a hyperplane, so 1 may occasionally be decrypted as 0.
8] , The hyperbolicity of the complement of 2n+1 hyperplanes in general position in [P.
If the statement about Lehmer's algorithm giving a sequence statistically indistinguishable from a sequence drawn at random without replacement were really true there would be no hyperplane problem, and that problem by itself can have practical consequences.
3GB/s HyperPlane architecture and 64-bit HP-UX 11 operating environment.
To study the interplay between various algebraic, geometric, and combinatorial aspects of real hyperplane arrangements, Aguiar and Mahajan present many new ideas and results, but also gather and organize material from various sources in the literature, sometimes highlighting previously unnoticed connections.

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