What does hyperplane mean?

Definitions for hyperplane
hy·per·plane

This dictionary definitions page includes all the possible meanings, example usage and translations of the word hyperplane.


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Wiktionary

  1. hyperplanenoun

    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)

Wikipedia

  1. Hyperplane

    In geometry, a hyperplane is a subspace whose dimension is one less than that of its ambient space. For example, if a space is 3-dimensional then its hyperplanes are the 2-dimensional planes, while if the space is 2-dimensional, its hyperplanes are the 1-dimensional lines. This notion can be used in any general space in which the concept of the dimension of a subspace is defined. In different settings, hyperplanes may have different properties. For instance, a hyperplane of an n-dimensional affine space is a flat subset with dimension n − 1 and it separates the space into two half spaces. While a hyperplane of an n-dimensional projective space does not have this property. The difference in dimension between a subspace S and its ambient space X is known as the codimension of S with respect to X. Therefore, a necessary and sufficient condition for S to be a hyperplane in X is for S to have codimension one in X.

Wikidata

  1. Hyperplane

    A hyperplane is a concept in geometry. It is a generalization of the plane into a different number of dimensions. 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.

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Numerology

  1. Chaldean Numerology

    The numerical value of hyperplane in Chaldean Numerology is: 7

  2. Pythagorean Numerology

    The numerical value of hyperplane in Pythagorean Numerology is: 3

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Translations for hyperplane

From our Multilingual Translation Dictionary

  • హైపర్ ప్లేన్Telugu

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"hyperplane." Definitions.net. STANDS4 LLC, 2024. Web. 28 Mar. 2024. <https://www.definitions.net/definition/hyperplane>.

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