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In mathematics, the affine hull or affine span of a set S in Euclidean space Rn is the smallest affine set containing S,[1] or equivalently, the intersection of all affine sets containing S. Here, an affine set may be defined as the translation of a vector subspace.
The affine hull aff(S) of S is the set of all affine combinations of elements of S, that is,
affinehull or affine span of a set S in Euclidean space Rn is the smallest affine set containing S, or equivalently, the intersection of all affine sets...
In mathematics, an affine combination of x1, ..., xn is a linear combination ∑ i = 1 n α i ⋅ x i = α 1 x 1 + α 2 x 2 + ⋯ + α n x n , {\displaystyle \sum...
extended from Euclidean spaces to arbitrary real vector spaces or affine spaces; convex hulls may also be generalized in a more abstract way, to oriented matroids...
vector bundle over an affine space is trivial. Affinehull – Smallest affine subspace that contains a subset Complex affine space – Affine space over the complex...
aircraft Hull (botany), the outer covering of seeds Hull (watercraft), the body or frame of a sea-going craft Submarine hullAffinehull, in affine geometry...
\operatorname {relint} (S)} ) is defined as its interior within the affinehull of S . {\displaystyle S.} In other words, relint ( S ) := { x ∈ S :...
closure of that linear span.) Affinehull Conical combination Convex hull Encyclopedia of Mathematics (2020). Linear Hull. Axler (2015) pp. 29-30, §§ 2...
triangulation for P if P is a set of points in general position; that is, the affinehull of P is d-dimensional and no set of d + 2 points in P lie on the boundary...
In geometry, a subset of a Euclidean space, or more generally an affine space over the reals, is convex if, given any two points in the subset, the subset...
subset of a vector space, the convex hull or affinehull of a subset of a vector space or the lower semicontinuous hull f ¯ {\displaystyle {\overline {f}}}...
which does not contain the origin, then the convex conical hull of S is a closed set. Affine combination Convex combination Linear combination Convex Analysis...
Extend each of the edges of the 5-cell to the line that contains it (its affinehull), similarly extend each triangle of the 5-cell to the 2-dimensional plane...
subject to this, maximizes c2Tx (lexicographic maximization). Find the affinehull of P. This also implies finding the dimension of P, and a point in the...
the convex hull of its k + 1 vertices. More formally, suppose the k + 1 points u 0 , … , u k {\displaystyle u_{0},\dots ,u_{k}} are affinely independent...
Affine arithmetic (AA) is a model for self-validated numerical analysis. In AA, the quantities of interest are represented as affine combinations (affine...
where aff ( A − A ) {\displaystyle \operatorname {aff} (A-A)} is the affinehull of A − A {\displaystyle A-A} (which is equal to span ( A − A ) {\displaystyle...
Geometry is one of the oldest mathematical sciences. Absolute geometry Affine geometry Algebraic geometry Analytic geometry Birational geometry Complex...
affine if Y {\displaystyle Y} has an open affine cover U i {\displaystyle U_{i}} 's such that f − 1 ( U i ) {\displaystyle f^{-1}(U_{i})} are affine....
used for affine spaces over an arbitrary field), the points whose all normalized barycentric coordinates are nonnegative form the convex hull of { A 0...
continuous functions is a convex cone. An affine convex cone is the set resulting from applying an affine transformation to a convex cone. A common example...
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