Definition of Hyperplane

1. Noun. (geometry) An ''n''-dimensional generalization of a plane; an affine subspace of dimension ''n-1'' that splits an ''n''-dimensional space. (In a one-dimensional space, it is a point; In two-dimensional space it is a line; In three-dimensional space, it is an ordinary plane) ¹

¹ Source:

Definition of Hyperplane

1. [n -S]

Hyperplane Pictures

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Lexicographical Neighbors of Hyperplane

hyperpipecolic acidemia
hyperplane (current term)
hyperplane eyepiece
hyperplastic arteriosclerosis
hyperplastic cholecystosis
hyperplastic gastric polyp
hyperplastic gingivitis
hyperplastic graft
hyperplastic inflammation
hyperplastic osteoarthritis
hyperplastic polyp

Literary usage of Hyperplane

Below you will find example usage of this term as found in modern and/or classical literature:

1. Geometry of Four Dimensions by Henry Parker Manning (1914)
"The hyperplane is therefore perpendicular to all of these elements (Art. 51, Th. 1, Cor.). If two elements in one of the two given planes are given as ..."

2. Mixture Models: Theory, Geometry, and Applications by Bruce G. Lindsay (1995)
"Thus this hyperplane is a support hyperplane, but not a very interesting one as far as ... In particular, if p is in Pr and lies in the hyperplane ..."

3. Higher Geometry: An Introduction to Advanced Methods in Analytic Geometry by Frederick Shenstone Woods (1922)
"A line is said to be perpendicular to a hyperplane when it is ... For this to happen it is necessary and sufficient that the hyperplane meet the hyperplane ..."

4. Convex Optimization & Euclidean Distance Geometry by Jon Dattorro (2005)
" PRINCIPLE 2: Supporting hyperplane The second most fundamental principle of convex geometry also follows from the geometric Hahn-Banach theorem [164 ..."

5. A Treatise on the Line Complex by Charles Minshall Jessop (1903)
"Any line which does not lie in a given hyperplane will obviously meet it iu one point only ; if two points of a line lie in a hyperplane the line will lie ..."

6. Genomic Signal Processing and Statistics by Edward R Dougherty (2005)
"The hyperplane is determined by the equation formed from setting the linear combination equal to 0. Using the dot product a which is equal to the sum in the ..."

7. Stochastic Inequalities by Moshe Shaked, Yung Liang Tong (1992)
"On the other hand, hyperplane bisection in a median sense is always possible for arbitrary (including atomic) probability measures in this setting. ..."

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