hyperplane

American  

[hahy-per-pleyn, hahy-per-pleyn] / ˈhaɪ pərˌpleɪn, ˌhaɪ pərˈpleɪn /

noun

Mathematics.

1. a subspace of a vector space that has dimension one less than the dimension of the vector space.

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hyperplane British  

/ ˈhaɪpəˌpleɪn /

noun

1. maths a higher dimensional analogue of a plane in three dimensions. It can be represented by one linear equation

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Etymology

Origin of hyperplane

First recorded in 1900–05; hyper- + plane ¹

Example Sentences

This function is an equation that describes where the hyperplane needs to be at each point in the planned trajectory so it remains collision-free.

From Science Daily • Mar. 7, 2024

Many safety check algorithms work by generating this hyperplane at a single point in time.

From Science Daily • Mar. 7, 2024

Instead, this new technique generates a hyperplane function that moves with the robot, so it can prove that an entire trajectory is collision-free rather than working one hyperplane at a time.

From Science Daily • Mar. 7, 2024

However, each time the robot moves, a new hyperplane needs to be recomputed to perform the safety check.

From Science Daily • Mar. 7, 2024

A linear complex is represented by a hyperplane section; and if two such complexes are in involution, the corresponding hyperplanes are conjugate with respect to the fundamental quadric.

From Encyclopaedia Britannica, 11th Edition, Volume 11, Slice 6 "Geodesy" to "Geometry" by Various