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affine space in a sentence


1) Every linear space is also an affine space .

affine collocations
2) A small virtual sphere was displayed at this location in affine space .

3) Projective space is a compact topological space, affine space is not.



affine space example sentences

4) Roughly, " affine spaces " are vector spaces whose origins are not specified.

5) Its generalization to convex functions of affine spaces is sometimes called the Legendre-Fenchel transformation.

6) Symmetric and locally symmetric spaces in general can be regarded as affine symmetric spaces .

7) An affine space is a non-compact manifold; a projective space is a compact manifold.

8) Informally, an affine space is a vector space without a fixed choice of origin.

9) More precisely, an affine space is a set with a free transitive vector space action.

10) Spacetime was described as an affine space with quadratic form in Minkowski space of 1908.

11) Shifting it by a vector external to it, one obtains an __FORMULA__-dimensional affine space .

12) That is, affine spaces are open subspaces of projective spaces, which are quotients of vector spaces.

13) An affine variety is a "rational variety" if it is birationally equivalent to an affine space .

14) Affine space is a geometry in this sense, and is equipped with a "flat" Cartan connection.

15) Thus a general affine manifold is viewed as "curved" deformation of the flat model geometry of affine space .



example sentences with affine space

16) In projective geometry, " affine space " means the complement of a hyperplane at infinity in a projective space.

17) An affine "n"-manifold is then a manifold which looks infinitesimally like "n"-dimensional affine space .

18) Its elements are the restrictions to "V" of the rational functions over the affine space containing "V".

19) In the words of John Baez, "an affine space is a vector space that's forgotten its origin".

20) An affine space , as with essentially any smooth Klein geometry, is a manifold equipped with a flat Cartan connection.

21) However, some one-dimensional subspaces are parallel to the affine space ; in some sense, they intersect it at infinity.

22) This defines only a partial function between affine spaces , which is defined only outside the hyperplane where the denominator is zero.

23) The confusion therefore arises because an affine space with a marked point can be identified with its tangent space at that point.

24) There is also (in two dimensions) a combinatorial generalization of coordinatized affine space , as developed in synthetic finite geometry.

25) The choice of the origin is arbitrary: any other point may be chosen, as the representation is of an affine space .

26) One can also understand "pure" rotations as linear maps in a vector space equipped with Euclidean structure, not as maps of points of a corresponding affine space .

27) Choosing an __FORMULA__-dimensional affine space as before one observes that the affine space is embedded as a proper subset into the projective space.

28) Choosing an __FORMULA__-dimensional affine space as before one observes that the affine space is embedded as a proper subset into the projective space.



How to use affine space in a sentence

29) Every point of the affine space is its intersection with a one-dimensional linear subspace (line through the origin) of the __FORMULA__-dimensional linear space.

30) When a manifold carries a spin"c" structure at all, the set of spin"c" structures forms an affine space .

31) More precisely, the space of the isomorphism classes of spin structures is an affine space over H1("M",Z2).

32) Corresponding concept in an affine space is a convex set, which allows only convex combinations (non-negative linear combinations that sum to 1).

33) Interval type variables are sometimes also called "scaled variables", but the formal mathematical term is an affine space (in this case an affine line).



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