## affine

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• Note there is a link between linear connection (also called affine connection) and a web.
• 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.
• Other methods can handle problems such as translation, scale, image rotation and even all affine transformations.
• Over the real affine plane the situation is more complicated.
• Unitary highest weight representations of the affine compact groups only exist when k is a natural number.
• Note that, unlike in the affine case, the midpoint between two points may not be uniquely determined.
• In affine space, the union of a line and a point not on the line is not equidimensional.
• In affine d-space, two flats of any dimension may be parallel.
• Thus the normal affine space is the plane of equation x=a.
• 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.
• In the more general situation, where the affine planes are not defined over a field, they will in general not be isomorphic.
• Every real (or complex) affine or projective space is also a topological space.
• The bias term allows us to make affine transformations to the data.

### Meaning of affine

• noun (anthropology) kin by marriage
• adjective (mathematics) of or pertaining to the geometry of affine transformations