Vector Space
A vector space over 
is a set of Vectors for which any Vectors 
, 
, and 
and any Scalars 
, 
have the followingproperties:
- 1. Commutativity:
- 2. Associativity of vector addition:
- 3. Additive identity: For all ,
- 4. Existence of additive inverse: For any , there exists a
such that 
- 5. Associativity of scalar multiplication:
- 6. Distributivity of scalar sums:
- 7. Distributivity of vector sums:
- 8. Scalar multiplication identity:
-D vector space of characteristic two has
distinct Subspaces of Dimension
.A Module is abstractly similar to a vector space, but it uses a Ring to defineCoefficients instead of the Field used for vector spaces. Modules haveCoefficients in much more general algebraic objects.
See also Banach Space, Field, Function Space, Hilbert Space, Inner Product Space, Module, Ring, Topological Vector Space
References
Arfken, G. Mathematical Methods for Physicists, 3rd ed. Orlando, FL: Academic Press, pp. 530-534, 1985.
- Transformation
- Transitive
- Transitive Closure
- Transitive Reduction
- Transitivity Class
- Translation
- Translation Relation
- Transpose
- Transpose Map
- Transposition
- Transposition Group
- Transposition Order
- Transversal Array
- Transversal Design
- Transversal Line
- Transylvania Lottery
- Trapdoor Function
- Trapezium
- Trapezohedron
- Trapezoid
- Trapezoidal Hexecontahedron
- Trapezoidal Icositetrahedron
- Trapezoidal Rule
- Traveling Salesman Constants
- Traveling Salesman Problem