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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 under positive scalar multiplication; that is, C {\displaystyle C} is a cone if x ∈ C {\displaystyle x\in C} implies s x ∈ C {\displaystyle sx\in C} for every positive scalar s {\displaystyle s} . This is…
The analysis highlights Products, Special examples and Definition as prominent areas in the source structure around Convex cone.
Source areas are shown by the number of related topics found in each part of the analysis. Use smaller areas too: they can reveal specialized angles and content gaps.
Smaller areas are not necessarily less important. They contain fewer connections in this analysis and can be useful for finding specialized angles or coverage gaps.
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The extracted context around Convex cone shows recurring relationship patterns in the source. For example, Convex cone → cone that is also closed under addition, set resulting from applying an affine transformation to a convex cone, special case of a linear cone as defined above.It follows from the above property that a convex cone can also be defined as a linear cone that is closed under convex combinations Another extracted example is Convex cone → Farkas, Half-spaces, Moreover. Use these groups to spot repeated connection types before inspecting the individual relationships.
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cone displaystyle convex vector space set cones subset linear closed positive polyhedral also defined definition called vectors every salient mathbb
TTTA extracted 16 structured relationships around Convex cone. Examples in this analysis include Convex cone → is a → cone that is also closed under addition and Convex cone → is a → special case of a linear cone as defined above.It follows from the above property that a convex cone can also be defined as a linear cone that is closed under convex combinations. The table shows each extracted connection, where it came from and its confidence.
| Subject | Predicate | Object | Confidence | Src |
|---|---|---|---|---|
| Convex cone | is a | cone that is also closed under addition | 0.90 | text |
| Convex cone | is a | special case of a linear cone as defined above.It follows from the above property that a convex cone can also be defined as a linear cone that is closed under convex combinations | 0.90 | text |
| Convex cone | is a | set resulting from applying an affine transformation to a convex cone | 0.90 | text |
| Convex cone | related to Affine convex cones | Technically | 0.60 | section |
| Convex cone | related to Blunt, pointed, flat, salient, and proper cones | According | 0.60 | section |
| Convex cone | related to Blunt, pointed, flat, salient, and proper cones | Blunt | 0.60 | section |
| Convex cone | related to Competing definitions | Therefore | 0.60 | section |
| Convex cone | related to Convex cone | Also | 0.60 | section |
| Convex cone | related to Dual cone | Consider | 0.60 | section |
| Convex cone | related to Face of a convex cone | Suppose | 0.60 | section |
| Convex cone | related to Half-spaces | Half-spaces | 0.60 | section |
| Convex cone | related to Half-spaces | Moreover | 0.60 | section |
The concept neighborhoods around Convex cone bring nearby vocabulary together. In this analysis, examples include Convex, Displaystyle and Set. Use the clusters to find adjacent concepts and terminology that may deserve separate research.
For Convex cone, one of the stronger structural bridges in this analysis connects Convex cone with Special examples. Bridges highlight paths between different parts of the map and can reveal research angles that are easy to miss in a flat list.
TTTA analyzes the structure around Convex cone to surface related topics, entities, relationships, concept neighborhoods and bridge connections. Use the map to explore areas such as Products, Special examples & Definition, including less central topics that may reveal useful research gaps. Automatically extracted connections are research leads rather than rewritten encyclopedia content.
Source: Wikipedia — Convex cone · EN edition · Analysis: TopicsToTalkAbout