## any affine

23 examples (0.01 sec)
• One can check that any affine involution in fact has this form.
• This means that one is free to apply any affine transformation to a polygon that might give it a more manageable form.
• Bent functions are in a sense equidistant from all the affine functions, so they are equally hard to approximate with any affine function.
• A scaling in the most general sense is any affine transformation with a diagonalizable matrix.
• Any affine subspace of the Euclidean n-dimensional space is also an example since the principal curvatures of any shape operator are zero.
• Geometrically this means that any affine involution can be obtained by taking oblique reflections against any number from 0 through n hyperplanes going through a point b.
• There are three families of polytopes which have simple representations in spaces, for any, and can be used to visualize any affine coordinate system in a real -space.
• In mathematics, the affine group or general affine group of any affine space over a field K is the group of all invertible affine transformations from the space into itself.
• For any affine algebraic set V, the coordinate ring or structure ring of V is the quotient of the polynomial ring by this ideal.
• Every bent function has a Hamming weight (number of times it takes the value 1) of, and in fact agrees with any affine function at one of those two numbers of points.
• Any affine curve X is isomorphic to an open subset of an integral projective (hence complete) curve.
• The Levi-Civita connection (like any affine connection) also defines a derivative along curves, sometimes denoted by D.
• This establishes that the above equation, clearly a generalization of the previous one, defines the Zariski topology on any affine variety.
• The aforementioned facts do not depend on the structure being that of Euclidean space (namely, involving Euclidean distance) and are correct in any affine space.
• Hence, the abovementioned formulas for Cartesian coordinates are applicable in any affine coordinate system.
• Conversely, any affine linear transformation extends uniquely to a projective linear transformations, so the affine group is a subgroup of the projective group.
• A system of coordinates on -dimensional space is defined by a (+1)-tuple of points not belonging to any affine subspace of a lesser dimension.
• Any affine group scheme is the spectrum of a commutative Hopf algebra (over a base S, this is given by the relative spectrum of an O S -algebra).
• Since straight lines are a concept in affine geometry, affine connections define a generalized notion of (parametrized) straight lines on any affine manifold, called affine geodesics.
• Unlike the Riemann curvature tensor or the Ricci tensor, which both can be naturally defined for any affine connection, the scalar curvature requires a metric of some kind.