On this page you'll find 2 example sentences with Hyperplanes. Discover the meaning, how to use the word correctly in a sentence.
Hyperplanes meaning
plural of hyperplane
Using Hyperplanes
- The main meaning on this page is: plural of hyperplane
Context around Hyperplanes
- Average sentence length in these examples: 43 words
- Position in the sentence: 0 start, 1 middle, 1 end
- Sentence types: 2 statements, 0 questions, 0 exclamations
Corpus analysis for Hyperplanes
- In this selection, "hyperplanes" usually appears in the middle of the sentence. The average example has 43 words, and this corpus slice is mostly made up of statements.
- Around the word, parallel stand out and add context to how "hyperplanes" is used.
- Recognizable usage signals include are parallel hyperplanes in v and of these hyperplanes. That gives this page its own corpus information beyond isolated example sentences.
- By corpus frequency, "hyperplanes" sits close to words such as aabc, aacr and aacsb, which helps place it inside the broader word index.
Example types with hyperplanes
The same corpus examples are grouped by length and sentence type, making it easier to see the contexts in which the word appears:
The vertices of one polytope correspond to the (n 1)-dimensional elements, or facets, of the other, and the j points that define a (j 1)-dimensional element will correspond to j hyperplanes that intersect to give a (n j)-dimensional element. (42 words)
More generally, if V is a vector space of any dimension, then the level sets of a linear functional in V ∗ are parallel hyperplanes in V, and the action of a linear functional on a vector can be visualized in terms of these hyperplanes. (44 words)
More generally, if V is a vector space of any dimension, then the level sets of a linear functional in V ∗ are parallel hyperplanes in V, and the action of a linear functional on a vector can be visualized in terms of these hyperplanes. (44 words)
The vertices of one polytope correspond to the (n 1)-dimensional elements, or facets, of the other, and the j points that define a (j 1)-dimensional element will correspond to j hyperplanes that intersect to give a (n j)-dimensional element. (42 words)
Example sentences (2)
More generally, if V is a vector space of any dimension, then the level sets of a linear functional in V ∗ are parallel hyperplanes in V, and the action of a linear functional on a vector can be visualized in terms of these hyperplanes.
The vertices of one polytope correspond to the (n 1)-dimensional elements, or facets, of the other, and the j points that define a (j 1)-dimensional element will correspond to j hyperplanes that intersect to give a (n j)-dimensional element.