Get to know Affine better with 10+ real example sentences, the meaning and synonyms like transformation or affinal.
Affine in a sentence
Affine meaning
- Assigning finite values to finite quantities.
- Of or pertaining to a function expressible as f(⃑x)=A⃑x+⃑b (where A is a linear transformation and ⃑b is a constant), which, regarded as a transformation, maps parallel lines to parallel lines and finite points to finite points.
- Of two materials, having mutual affinity.
Synonyms of Affine
Using Affine
- The main meaning on this page is: Assigning finite values to finite quantities. | Of or pertaining to a function expressible as f(⃑x)=A⃑x+⃑b (where A is a linear transformation and ⃑b is a constant), which, regarded as a transformation, maps parallel lines to parallel lines and finite points to finite points. | Of two materials, having mutual affinity.
- Useful related words include: transformation, affinal, related, kin.
- In the example corpus, affine often appears in combinations such as: an affine, affine transformation, affine transformations.
Context around Affine
- Average sentence length in these examples: 23.9 words
- Position in the sentence: 10 start, 9 middle, 1 end
- Sentence types: 20 statements, 0 questions, 0 exclamations
Corpus analysis for Affine
- In this selection, "affine" usually appears near the start of the sentence. The average example has 23.9 words, and this corpus slice is mostly made up of statements.
- Around the word, simple, transformations, commonplace, transformation, transformations and space stand out and add context to how "affine" is used.
- Recognizable usage signals include is an affine n 1, a finite affine plane when and affine transformation. That gives this page its own corpus information beyond isolated example sentences.
- By corpus frequency, "affine" sits close to words such as aadmi, aang and ably, which helps place it inside the broader word index.
Example types with affine
The same corpus examples are grouped by length and sentence type, making it easier to see the contexts in which the word appears:
Affine transformation of the plane A central dilation. (8 words)
An affine transformation is invertible if and only if is invertible. (11 words)
Affine planes Projectivization of the Euclidean plane produced the real projective plane. (12 words)
There is a projective plane of order N if and only if there is an affine plane of order N. When there is only one affine plane of order N there is only one projective plane of order N, but the converse is not true. (45 words)
This is a special case of conical (perspective) projection of any of those geometric objects in the affine space from a point O onto a plane P, when the point O lies in the plane at infinity of the affine space. (41 words)
Also, both curves are rational, as they are parameterized by x, and Riemann-Roch theorem implies that the cubic curve must have a singularity, which must be at infinity, as all its points in the affine space are regular. (39 words)
Example sentences (20)
Affine transformation in plane geometry A simple affine transformation on the real plane Effect of applying various 2D affine transformation matrices on a unit square.
Examples of affine transformations Affine transformations over the real numbers Functions with and constant, are commonplace affine transformations.
Affine scaling main Affine scaling is one of the oldest interior point methods to be developed.
Affine space An ellipse is also the result of projecting a circle, sphere, or ellipse in a three dimensional affine space onto a plane (flat), by parallel lines.
All Euclidean spaces are affine, but there are affine spaces that are non-Euclidean.
Mathematical definition An affine map between two affine spaces is a map on the points that acts linearly on the vectors (that is, the vectors between points of the space).
Note that each facet of an n-simplex is an affine n-1-simplex, and thus the boundary of an n-simplex is an affine n-1-chain.
There is a projective plane of order N if and only if there is an affine plane of order N. When there is only one affine plane of order N there is only one projective plane of order N, but the converse is not true.
This is a special case of conical (perspective) projection of any of those geometric objects in the affine space from a point O onto a plane P, when the point O lies in the plane at infinity of the affine space.
Thus, every linear transformation is affine, but not every affine transformation is linear.
A commonly used method for carrying out the embedding in this case involves expanding the set of affine coordinates and working in a more general "algebra".
Affine planes Projectivization of the Euclidean plane produced the real projective plane.
Affine scaling amounts to doing gradient descent steps within the feasible region, while rescaling the problem to make sure the steps move toward the optimum faster.
Affine transformation of the plane A central dilation.
Affine transformations such as translation and rotation can be applied on the curve by applying the respective transform on the control points of the curve.
A finite projective plane will produce a finite affine plane when one of its lines and the points on it are removed.
All of these concepts are usually defined as subsets of an ambient vector space (except for affine spaces, which are also considered as "vector spaces forgetting the origin"), rather than being axiomatized independently.
Also, both curves are rational, as they are parameterized by x, and Riemann-Roch theorem implies that the cubic curve must have a singularity, which must be at infinity, as all its points in the affine space are regular.
An affine transformation is invertible if and only if is invertible.
An example of a non-unimodular group is the group of affine transformations : on the real line.
Phrases with affine
These phrases have their own page with example sentences containing the full combination:
Common combinations with affine
These word pairs occur most frequently in English texts: