Category:Definitions/Examples of Vector Spaces
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This category contains definitions of examples of Vector Space.
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 3 subcategories, out of 3 total.
C
R
Pages in category "Definitions/Examples of Vector Spaces"
The following 14 pages are in this category, out of 14 total.
D
V
- Definition:Vector Space of All Mappings
- Definition:Vector Space of Matrices
- Definition:Vector Space of Sequences with Finite Support
- Definition:Vector Space on Cartesian Product
- Definition:Vector Space on Field Extension
- Definition:Vector Space over Division Subring
- Definition:Vector Space over Division Subring/Special Case
- Definition:Vector Space over Subring