hyperplane

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• hyperplane — [hī′pər plān΄] n. Math. an analogue of a plane in a space of four or more dimensions …   English World dictionary

• Hyperplane — A hyperplane is a concept in geometry. It is a higher dimensional generalization of the concepts of a line in Euclidean plane geometry and a plane in 3 dimensional Euclidean geometry. The most familiar kinds of hyperplane are affine and linear… …   Wikipedia

• hyperplane — hiperplokštuma statusas T sritis fizika atitikmenys: angl. hyperplane vok. Hyperebene, f rus. гиперплоскость, f pranc. hyperplan, m …   Fizikos terminų žodynas

• Hyperplane at infinity — In mathematics, in particular projective geometry, the hyperplane at infinity, also called the ideal hyperplane, is an ( n −1) dimensional projective space added to an n dimensional affine space A, such as the real affine n space mathbb{R}^n , in …   Wikipedia

• Hyperplane section — In mathematics, a hyperplane section of a subset X of projective space P n is the intersection of X with some hyperplane H mdash; in other words we look at the subset X H of those elements x of X that satisfy the single linear condition L = 0… …   Wikipedia

• hyperplane — noun Date: 1903 a figure in hyperspace corresponding to a plane in ordinary space …   New Collegiate Dictionary

• hyperplane — /huy peuhr playn , huy peuhr playn /, n. Math. a subspace of a vector space that has dimension one less than the dimension of the vector space. [1900 05; HYPER + PLANE1] * * * …   Universalium

• hyperplane — noun 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… …   Wiktionary

• hyperplane — hy·per·plane …   English syllables

• hyperplane — | ̷ ̷ ̷ ̷+ noun Etymology: hyper + plane : a figure in hyperspace corresponding to a plane in ordinary space * * * /huy peuhr playn , huy peuhr playn /, n. Math. a subspace of a vector space that has dimension one less than the dimension of the… …   Useful english dictionary

• Supporting hyperplane — is a concept in geometry. A hyperplane divides a space into two half spaces. A hyperplane is said to support a set S in Euclidean space mathbb R^n if it meets both of the following: * S is entirely contained in one of the two closed half spaces… …   Wikipedia