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hyperplane's Usage Examples:

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

(called branches) representing the spatial relations between a collection of mirrors (or reflecting hyperplanes).

Cartesian coordinates, such a hyperplane can be described with a single linear equation of the following form (where at least one of the a i {\displaystyle.

N is a normal vector of this hyperplane.

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

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

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

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

The theorem of Bertini states that the set of hyperplanes not containing X and with smooth intersection with X contains an open.

Questions about a hyperplane arrangement.

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).

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