Linear and multilinear algebra; matrix theory Vector spaces Concept
Vector space
Summary
A vector space over a field is a set of vectors that can be added and multiplied by scalars, with the usual rules of arithmetic. Vector spaces are the main objects of linear algebra.
Where this leads
58 pages build on this one.
- Cap set problem
- Functional
- Positive linear operator
- Clifford algebra
- Unisolvent point set
- First variation
- Path algebra
- Affine space as an algebra
- Face of a convex set
- Elementary abelian group
- Open segment
- Multicategory
- Sublinear function
- Topological vector space
- Persistent homology
- Banach limit
- Quadric
- Essentially surjective functor
- Natural transformation
- Rota's basis conjecture
- Pointed cone
- Minkowski addition
- M. Riesz extension theorem
- Zariski tangent space
- Polarity
- Projective space
- Convex combination
- Lattice of subspaces
- Convex cone
- Comodule
- Equivalence of categories
- Growth of algebras
- Extreme set
- Dual operator
- Convex join
- Whitney sum
- Veblen–Young theorem
- Coalgebra
- Lorentz's characterization of almost convergence
- Convex independence
- Geometric algebra
- Hahn–Banach theorem
- Representation of a quiver
- Group representation
- Group algebra
- Tensor rank
- Cotangent space of a local ring
- Sullivan minimal model
- Irreducible representation
- Extreme point
- Slice theorem
- Tensor algebra
- Section of a vector bundle
- Hodge structure
- Gelfand–Kirillov dimension
- Symmetric algebra
- Line segment
- Tensor decomposition
Further reading
- Web https://en.wikipedia.org/wiki/Vector_space, Definition and basic properties
About this page
| Tag | 000AYPA9AJ |
|---|---|
| URI | m2://000AYPA9AJ |
| Aliases | linear-space |
| Kind | concept |
| Writing | W1 stated |
| MSC | 15A03 |
| Specializes | Module over a ring |
| Same as |
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What this page needs for W2
- edge not_instance_of in: at least one non-example (0 of 1)
The writing levels say how complete the text of a page is. They do not measure its truth.
What links here
Special cases
- Linear subspace
- Dual space
- Tensor product of vector spaces
- Quotient space
- Product of vector spaces
- Inner product space
- External direct sum
- Space of linear maps
- Finite-dimensional vector space
- Ordered vector space
- Symplectic vector space
- Topological vector space
Definitions
Instances
Used by
- Cap set problem
- Functional
- Positive linear operator
- Clifford algebra
- Unisolvent point set
- First variation
- Path algebra
- Affine space as an algebra
- Face of a convex set
- Elementary abelian group
- Open segment
- Multicategory
- Sublinear function
- Topological vector space
- Persistent homology
- Quadric
- Essentially surjective functor
- Natural transformation
- Rota's basis conjecture
- Pointed cone
- Minkowski addition
- M. Riesz extension theorem
- Zariski tangent space
- Polarity
- Projective space
- Convex combination
- Lattice of subspaces
- Convex cone
- Comodule
- Equivalence of categories
- Growth of algebras
- Extreme set
- Convex join
- Whitney sum
- Veblen–Young theorem
- Coalgebra
- Convex independence
- Geometric algebra
- Hahn–Banach theorem
- Representation of a quiver
- Group representation
- Group algebra
- Tensor rank
- Cotangent space of a local ring
- Irreducible representation
- Extreme point
- Tensor algebra
- Section of a vector bundle
- Hodge structure
- Gelfand–Kirillov dimension
- Symmetric algebra
- Line segment
- Tensor decomposition