Dual cone and polar cone are closely related concepts in convex analysis, a branch of mathematics. The dual cone C* of a subset C in a linear space X over...

In linear algebra, a cone—sometimes called a linear cone to distinguish it from other sorts of cones—is a subset of a real vector space that is closed...

dual cone and polar cone one can consider the polar duality for reflexive polytopes as a special case of the duality for convex Gorenstein cones and of...

dual relationship for a hyperplane yields that hyperplane's polar point.[citation needed] Some authors (confusingly) call a dual cone the polar cone;...

body and polar body. Dual abelian variety Dual basis Dual (category theory) Dual code Duality (electrical engineering) Duality (optimization) Dualizing module...

In mathematics, symmetric cones, sometimes called domains of positivity, are open convex self-dual cones in Euclidean space which have a transitive group...

convex cone generated by a generator of the Lie algebra of the center is closed and is the minimal invariant convex cone (up to a sign). The dual cone with...

with positive cone C , {\displaystyle C,} called the dual cone and denoted by C ∗ , {\displaystyle C^{*},} is a cone equal to the polar of − C . {\displaystyle...

(that is, the polar of the polar) of a set. In convex analysis, the bipolar theorem refers to a necessary and sufficient conditions for a cone to be equal...

barrier cone is a cone associated to any non-empty subset of a Banach space. It is closely related to the notions of support functions and polar sets. Let...

curve obtained from a cone's surface intersecting a plane. The three types of conic section are the hyperbola, the parabola, and the ellipse; the circle...

normal fan of P can be constructed from the polar dual of P by taking the cone over each face of the dual polytope, P°. For f a polynomial in n variables...

generator line, a line containing the apex and a point on the cone surface) m 0 {\displaystyle m_{0}} of the cone, is a parabola (red curve in the diagram)...

equivalent Shadow price Dual cone and polar cone Duality gap — difference between primal and dual solution Fenchel's duality theorem — relates minimization...

additional cone called a whizzer: a small, light cone attached to the joint between the voice coil and the primary cone. The whizzer cone extends the...

curve to its dual, sending each point to the point dual to its tangent line. If C is algebraic then so is its dual and the degree of the dual is known as...

with positive cone C , {\displaystyle C,} called the dual cone and denoted by C ∗ , {\displaystyle C^{*},} is a cone equal to the polar of − C . {\displaystyle...

hollow cone of light. There are two possible conical refractions, one internal and one external. For internal refraction, there are 4 directions, and for...

generates a polar raster in the frequency domain. The polar raster is sparse, so interpolation is used to fill the unknown DFT points, and reconstruction...

coupling the cone of the speaker to the voice coil bobbin through a compliant section and directly attaching a small lightweight whizzer cone to the bobbin...

near which K looks like a quadratic cone. Any projective line through p then meets K with multiplicity two at p, and will therefore meet the quartic K in...

55, 231) apolar Orthogonal under the polar pairing between the symmetric algebra of a vector space and its dual. arithmetic genus The arithmetic genus...

Cross section Crystal Cuisenaire rods Desargues' theorem Right circular cone Hyperboloid Napkin ring problem Pappus's centroid theorem Paraboloid Polyhedron...

flowering plants, or from the male cone to the female cone of gymnosperms. If pollen lands on a compatible pistil or female cone, it germinates, producing a...

patterns following the diurnal cycles. The shape of the gland resembles a pine cone, which gives it its name. The pineal gland is located in the epithalamus...

turn round and round." The word was used both by Euclid and Archimedes, who used the term "solid rhombus" for a bicone, two right circular cones sharing...

pole). Poles and polars have several useful properties: If a point P lies on a line l, then the pole L of the line l lies on the polar p of point P....

represented exactly as a closed-form expression. Any canonical polyhedron and its polar dual can be used to form two opposite faces of a four-dimensional antiprism...

denoted by C ∗ , {\displaystyle C^{*},} is a cone equal to the polar of − C . {\displaystyle -C.} The order dual of an ordered vector space X {\displaystyle...

Atmospheric molecules can also escape from the polar regions on a planet with a magnetosphere, due to the polar wind. Near the poles of a magnetosphere, the...