hyperplane's Usage Examples:

geometry, a hyperplane is a subspace whose dimension is one less than that of its ambient space.

If a space is 3-dimensional then its hyperplanes are the.

In geometry, the hyperplane separation theorem is a theorem about disjoint convex sets in n-dimensional Euclidean space.

the two parts into which a hyperplane divides an affine space.

That is, the points that are not incident to the hyperplane are partitioned into two convex.

hyperplane.

There are many hyperplanes that might classify the data.

One reasonable choice as the best hyperplane.

sometimes represented as a hyperplane in space-time, typically called "now", although modern physics demonstrates that such a hyperplane cannot be defined uniquely.

a mapping from a Euclidean space to itself that is an isometry with a hyperplane as a set of fixed points; this set is called the axis (in dimension 2).

arrangement of hyperplanes is an arrangement of a finite set A of hyperplanes in a linear, affine, or projective space S.

Questions about a hyperplane arrangement.

budget sets and convex preferences: At equilibrium prices, the budget hyperplane supports the best attainable indifference curve.

geometry, a supporting hyperplane of a set S {\displaystyle S} in Euclidean space R n {\displaystyle \mathbb {R} ^{n}} is a hyperplane that has both of the.

In geometry, a hypersurface is a generalization of the concepts of hyperplane, plane curve, and surface.

specifically in algebraic geometry and algebraic topology, the Lefschetz hyperplane theorem is a precise statement of certain relations between the shape.

dual of the hyperplane bundle or Serre's twisting sheaf O P n ( 1 ) {\displaystyle {\mathcal {O}}_{\mathbb {P} ^{n}}(1)} .

The hyperplane bundle is the.

some hyperplane orthogonal to a line joining opposite vertices of one of the 24-cells.

For instance, one could take any of the coordinate hyperplanes in.

is replaced by a hyperplane.

The problem of determining if a pair of sets is linearly separable and finding a separating hyperplane if they are, arises.

that projective space that leave the hyperplane at infinity invariant, restricted to the complement of that hyperplane.

}}={\frac {dw}{d\tau }},} then they share the same simultaneous hyperplane.

This hyperplane exists mathematically, but physical relations in relativity involve.

a linear transformation that describes a reflection about a plane or hyperplane containing the origin.

limit of a sequence of increasing balls sharing (on one side) a tangent hyperplane and its point of tangency.

basis of the ambient space is a vector hyperplane.

In a vector space of finite dimension n, a vector hyperplane is thus a subspace of dimension n – 1.

n-dimensional distance from that datum to the separating hyperplane.