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 50 subcategories, out of 50 total.
A
- Absorbent Sets (empty)
B
C
- Convex Cones (1 P)
D
- Dilation Mappings (2 P)
E
F
- Fredholm Operators (3 P)
G
H
- Hyperplanes (2 P)
I
L
M
N
- Norms on Vector Spaces (empty)
O
- Orthogonal Complements (empty)
P
- Positive Definite Vector Spaces (empty)
Q
- Quasinorms (1 P)
S
- Scalar Addition (empty)
- Seminorms (15 P)
- Standard Ordered Bases (5 P)
T
V
- Vector Space Automorphisms (2 P)
Pages in category "Vector Spaces"
The following 40 pages are in this category, out of 40 total.
C
D
F
I
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
T
V
- Vector Augend plus Addend equals Augend implies Addend is Zero
- Vector Space has Unique Additive Identity
- Vector Space is Affine Space
- Definition:Vector Space of All Mappings
- Vector Space of Continuous on Closed Interval Real Functions is not Finite Dimensional
- Definition:Vector Space of Germs of Smooth Functions
- Definition:Vector Space of Sequences with Finite Support