How do you use Collineation in a sentence? See 6 example sentences showing how this word appears in different contexts, plus the exact meaning.
Collineation meaning
- The act of collineating; collimation.
- An isomorphism from one projective space to another, often to itself.
Using Collineation
- The main meaning on this page is: The act of collineating; collimation. | An isomorphism from one projective space to another, often to itself.
- In the example corpus, collineation often appears in combinations such as: of collineation.
Context around Collineation
- Average sentence length in these examples: 27 words
- Position in the sentence: 2 start, 1 middle, 3 end
- Sentence types: 6 statements, 0 questions, 0 exclamations
Corpus analysis for Collineation
- In this selection, "collineation" usually appears near the end of the sentence. The average example has 27 words, and this corpus slice is mostly made up of statements.
- Around the word, nontrivial, group, form and either stand out and add context to how "collineation" is used.
- Recognizable usage signals include a nontrivial collineation and called a collineation or symmetry. That gives this page its own corpus information beyond isolated example sentences.
- By corpus frequency, "collineation" sits close to words such as aaaaa, aage and aardvarks, which helps place it inside the broader word index.
Example types with collineation
The same corpus examples are grouped by length and sentence type, making it easier to see the contexts in which the word appears:
If a correlation φ is not a polarity then φ 2 is a nontrivial collineation. (15 words)
Another type of collineation of PG(2,K) is induced by any automorphism of K, these are called automorphic collineations. (20 words)
Thus, the fixed point and fixed line structure for any collineation either form a projective plane by themselves, or a degenerate plane. (22 words)
The collection of fixed points and fixed lines of a collineation form a closed configuration, which is a system of points and lines that satisfy the first two but not necessarily the third condition in the definition of a projective plane. (41 words)
The affine planes formed by the removal of different lines of the projective plane will be isomorphic if and only if the removed lines are in the same orbit of the collineation group of the projective plane. (37 words)
A permutation of the seven points that carries collinear points (points on the same line) to collinear points is called a collineation or symmetry of the plane. (27 words)
Example sentences (6)
Another type of collineation of PG(2,K) is induced by any automorphism of K, these are called automorphic collineations.
A permutation of the seven points that carries collinear points (points on the same line) to collinear points is called a collineation or symmetry of the plane.
If a correlation φ is not a polarity then φ 2 is a nontrivial collineation.
The affine planes formed by the removal of different lines of the projective plane will be isomorphic if and only if the removed lines are in the same orbit of the collineation group of the projective plane.
The collection of fixed points and fixed lines of a collineation form a closed configuration, which is a system of points and lines that satisfy the first two but not necessarily the third condition in the definition of a projective plane.
Thus, the fixed point and fixed line structure for any collineation either form a projective plane by themselves, or a degenerate plane.
Common combinations with collineation
These word pairs occur most frequently in English texts:
- of collineation 2×