Category:Vector Spaces
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This category contains results about Vector Spaces.
Definitions specific to this category can be found in Definitions/Vector Spaces.
Let $\struct {K, +_K, \times_K}$ be a field.
Let $\struct {G, +_G}$ be an abelian group.
Let $\struct {G, +_G, \circ}_K$ be a unitary $K$-module.
Then $\struct {G, +_G, \circ}_K$ is a vector space over $K$ or a $K$-vector space.
That is, a vector space is a unitary module whose scalar ring is a field.
Subcategories
This category has the following 35 subcategories, out of 35 total.
A
B
- Balanced Sets (12 P)
C
D
- Dilation Mappings (2 P)
E
G
H
- Hyperplanes (2 P)
I
L
- Linear Independence (12 P)
- Locally Convex Spaces (15 P)
N
Q
- Quasinorms (1 P)
S
- Scalar Addition (empty)
- Seminorms (11 P)
- Standard Ordered Bases (5 P)
T
V
Pages in category "Vector Spaces"
The following 30 pages are in this category, out of 30 total.
C
S
- Set of Vectors defined by Directed Line Segments in Space forms Vector Space
- Singleton is Convex Set
- Size of Linearly Independent Subset is at Most Size of Finite Generator
- Space of Real-Valued Measurable Functions Identified by A.E. Equality is Vector Space
- Star Convex Set is Path-Connected
- Star Convex Set is Simply Connected
- Sum of Union of Subsets of Vector Space and Subset