an affine

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• An affine resource can only be used once, while a linear one must be used once.
• In an affine space, there is no distinguished point that serves as an origin.
• In particular, a vector space is an affine space over itself, by the map.
• More generally, a half-space is either of the two parts into which a hyperplane divides an affine space.
• In an affine space, there are instead displacement vectors between two points of the space.
• Also, sets of parallel lines remain parallel after an affine transformation.
• The confusion therefore arises because an affine space with a marked point can be identified with its tangent space at that point.
• Every linear space is also an affine space.
• Informally, an affine space is a vector space without a fixed choice of origin.
• An ellipse can be seen as an image of the unit circle under an affine transformation.
• Let G be a unipotent group acting on an affine variety.
• An affine transformation is fit between the image of the currently tracked feature and its image from a non-consecutive previous frame.
• This is necessary if one wanted the quotient to be an affine algebraic variety.
• More precisely, an affine space is a set with a free transitive vector space action.
• Then the set complement is called an affine space.
• In an affine plane the parallel relation between lines is essential.
• For any isometry group in Euclidean space the set of fixed points is either empty or an affine space.
• This is because the horseshoe maps the left cap into itself by an affine transformation that has exactly one fixed point.
• Similarly, starting from an affine space A, every class of parallel lines can be associated with a point at infinity.
• When a manifold carries a spin c structure at all, the set of spin c structures forms an affine space.