hyperplane

American

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

noun

Mathematics.

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

hyperplane British

/ ˈhaɪpəˌpleɪn /

noun

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

"Collins English Dictionary — Complete & Unabridged" 2012 Digital Edition © William Collins Sons & Co. Ltd. 1979, 1986 © HarperCollins Publishers 1998, 2000, 2003, 2005, 2006, 2007, 2009, 2012

Etymology

Origin of hyperplane

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

Example Sentences

Examples are provided to illustrate real-world usage of words in context. Any opinions expressed do not reflect the views of Dictionary.com.

By double-checking that the hyperplane function contains squared values, a human can easily verify that the function is positive, which means the trajectory is collision-free, Amice explains.

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

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

From Science Daily • Mar. 7, 2024

Mathematically, this piece of paper is called a hyperplane.

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

Definitions and idiom definitions from Dictionary.com Unabridged, based on the Random House Unabridged Dictionary, © Random House, Inc. 2023