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- Cone_(linear_algebra) abstract "In linear algebra, a (linear) cone is a subset of a vector space that is closed under multiplication by positive scalars. In other words, a subset C of a real vector space V is a cone if and only if λx belongs to C for any x in C and any positive scalar λ of V (or, more succinctly, if and only if λC = C for any positive scalar λ). A cone is said to be pointed if it includes the null vector (origin) 0; otherwise it is said to be blunt. Some authors use "non-negative" instead of "positive" in this definition of "cone", which restricts the term to the pointed cones only. In other contexts, a cone is pointed if the only linear subspace contained in it is {0}.The definition makes sense for any vector space V which allows the notion of "positive scalar" (i.e., where the ground field is an ordered field), such as spaces over the rational, real algebraic, or (most commonly) real numbers.The concept can also be extended for any vector space V whose scalar field is a superset of those fields (such as the complex numbers, quaternions, etc.), to the extent that such a space can be viewed as a real vector space of higher dimension.".
- Cone_(linear_algebra) wikiPageID "1503234".
- Cone_(linear_algebra) wikiPageLength "4945".
- Cone_(linear_algebra) wikiPageOutDegree "39".
- Cone_(linear_algebra) wikiPageRevisionID "675418170".
- Cone_(linear_algebra) wikiPageWikiLink Affine_variety.
- Cone_(linear_algebra) wikiPageWikiLink Algebra_of_sets.
- Cone_(linear_algebra) wikiPageWikiLink Algebraic_geometry.
- Cone_(linear_algebra) wikiPageWikiLink Algebraic_number.
- Cone_(linear_algebra) wikiPageWikiLink Bijection.
- Cone_(linear_algebra) wikiPageWikiLink Category:Geometric_shapes.
- Cone_(linear_algebra) wikiPageWikiLink Category:Linear_algebra.
- Cone_(linear_algebra) wikiPageWikiLink Central_projection.
- Cone_(linear_algebra) wikiPageWikiLink Closed_(mathematics).
- Cone_(linear_algebra) wikiPageWikiLink Closed_(topology).
- Cone_(linear_algebra) wikiPageWikiLink Closed_set.
- Cone_(linear_algebra) wikiPageWikiLink Complement_(set_theory).
- Cone_(linear_algebra) wikiPageWikiLink Complex_number.
- Cone_(linear_algebra) wikiPageWikiLink Cone.
- Cone_(linear_algebra) wikiPageWikiLink Cone_(disambiguation).
- Cone_(linear_algebra) wikiPageWikiLink Cone_(geometry).
- Cone_(linear_algebra) wikiPageWikiLink Cone_(topology).
- Cone_(linear_algebra) wikiPageWikiLink Conic_combination.
- Cone_(linear_algebra) wikiPageWikiLink Conical_combination.
- Cone_(linear_algebra) wikiPageWikiLink Convex_cone.
- Cone_(linear_algebra) wikiPageWikiLink Half-space_(geometry).
- Cone_(linear_algebra) wikiPageWikiLink Intersection_(set_theory).
- Cone_(linear_algebra) wikiPageWikiLink Linear_algebra.
- Cone_(linear_algebra) wikiPageWikiLink Linear_map.
- Cone_(linear_algebra) wikiPageWikiLink Multiplication.
- Cone_(linear_algebra) wikiPageWikiLink Norm_(mathematics).
- Cone_(linear_algebra) wikiPageWikiLink Null_vector.
- Cone_(linear_algebra) wikiPageWikiLink Null_vector_(vector_space).
- Cone_(linear_algebra) wikiPageWikiLink Ordered_field.
- Cone_(linear_algebra) wikiPageWikiLink Ordered_group.
- Cone_(linear_algebra) wikiPageWikiLink Ordered_vector_space.
- Cone_(linear_algebra) wikiPageWikiLink Origin_(mathematics).
- Cone_(linear_algebra) wikiPageWikiLink Partially_ordered_group.
- Cone_(linear_algebra) wikiPageWikiLink Projection_(mathematics).
- Cone_(linear_algebra) wikiPageWikiLink Projective_variety.
- Cone_(linear_algebra) wikiPageWikiLink Quaternion.
- Cone_(linear_algebra) wikiPageWikiLink Rational_number.
- Cone_(linear_algebra) wikiPageWikiLink Real_number.
- Cone_(linear_algebra) wikiPageWikiLink Scalar_(mathematics).
- Cone_(linear_algebra) wikiPageWikiLink Set_complement.
- Cone_(linear_algebra) wikiPageWikiLink Set_union.
- Cone_(linear_algebra) wikiPageWikiLink Sphere.
- Cone_(linear_algebra) wikiPageWikiLink Subset.
- Cone_(linear_algebra) wikiPageWikiLink Topology.
- Cone_(linear_algebra) wikiPageWikiLink Union_(set_theory).
- Cone_(linear_algebra) wikiPageWikiLink Vector_space.
- Cone_(linear_algebra) wikiPageWikiLinkText "Cone (linear algebra)".
- Cone_(linear_algebra) wikiPageWikiLinkText "Cone (linear algebra)#Affine cone".
- Cone_(linear_algebra) wikiPageWikiLinkText "cone (linear algebra)".
- Cone_(linear_algebra) wikiPageWikiLinkText "cone".
- Cone_(linear_algebra) wikiPageWikiLinkText "cones".
- Cone_(linear_algebra) wikiPageWikiLinkText "conical".
- Cone_(linear_algebra) wikiPageWikiLinkText "convex cone".
- Cone_(linear_algebra) wikiPageWikiLinkText "linear cone".
- Cone_(linear_algebra) wikiPageWikiLinkText "pointed cone".
- Cone_(linear_algebra) hasPhotoCollection Cone_(linear_algebra).
- Cone_(linear_algebra) wikiPageUsesTemplate Template:Functional_Analysis.
- Cone_(linear_algebra) wikiPageUsesTemplate Template:Unreferenced.
- Cone_(linear_algebra) subject Category:Geometric_shapes.
- Cone_(linear_algebra) subject Category:Linear_algebra.
- Cone_(linear_algebra) hypernym Subset.
- Cone_(linear_algebra) type Software.
- Cone_(linear_algebra) comment "In linear algebra, a (linear) cone is a subset of a vector space that is closed under multiplication by positive scalars. In other words, a subset C of a real vector space V is a cone if and only if λx belongs to C for any x in C and any positive scalar λ of V (or, more succinctly, if and only if λC = C for any positive scalar λ). A cone is said to be pointed if it includes the null vector (origin) 0; otherwise it is said to be blunt.".
- Cone_(linear_algebra) label "Cone (linear algebra)".
- Cone_(linear_algebra) sameAs Kegel_(Lineare_Algebra).
- Cone_(linear_algebra) sameAs Cône_(analyse_convexe).
- Cone_(linear_algebra) sameAs Cono_(algebra_lineare).
- Cone_(linear_algebra) sameAs m.056f99.
- Cone_(linear_algebra) sameAs Q493171.
- Cone_(linear_algebra) sameAs Q493171.
- Cone_(linear_algebra) wasDerivedFrom Cone_(linear_algebra)?oldid=675418170.
- Cone_(linear_algebra) isPrimaryTopicOf Cone_(linear_algebra).