Definitions

from Wiktionary, Creative Commons Attribution/Share-Alike License

  • n. 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)

from The Century Dictionary and Cyclopedia

  • n. An (n—1)-dimensional plane, defined in n-dimensional space by a homogeneous linear equation between its homogeneous coördinates.

Etymologies

Sorry, no etymologies found.

Examples

  • Alternatively, you could use discriminant analysis: find the hyperplane in role playing, sexual orientation, minority group space that best separates those with mental health problems from those without.

    Role Player Study released

  • We want to see Richard Seaton blow up the Fenacrhone space-battlewagon with his third-order zone of force, assuming he can escape from the fourth-dimensional evil of the hyperplane.

    Rothfuss on Genre Fiction

  • In any case, Myrvold's proposal demonstrates that even if state collapses are not hyperplane dependent, they need not be incompatible with relativity theory.

    Action at a Distance in Quantum Mechanics

  • The hyperplane-dependent theory is genuinely relativistic.

    Action at a Distance in Quantum Mechanics

  • This time, I could clearly see the sphere, extending "above" and "below" the hyperplane of three-dimensional space in smooth hemispheres.

    Orphans of Chaos

  • Phillips seems to go further and say something to the effect that any vector of random noise can be explained presumably meaning something other than the trivial “you pick the significance of the explanation, and I pick an explaining hyperplane”.

    Spurious Significance #1 « Climate Audit

  • Their little hyperplane was skimming at the brink of space, and the crew was locked inside the cockpit, and the two of them were sharing the little foldout bed.

    Asimov's Science Fiction

  • The Unit Theorem implies that this map has the roots of unity as kernel and maps '' U '' to a lattice of full rank in a hyperplane.

    Citizendium, the Citizens' Compendium - Recent changes [en]

  • Each of the training examples which supports the dividing line (or more accurately the dividing hyperplane) has a value in the array lagrangeMults which effectively defines it's weight.

    Planet PHP

  • We know that this value must lie on the decision hyperplane, so we can substitute it into the hyperplane equation, then shuffle it around to solve for r:

    Planet PHP

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