# Category:Examples of Vector Spaces

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This category contains 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.

## Pages in category "Examples of Vector Spaces"

The following 28 pages are in this category, out of 28 total.

### C

### R

### S

- Space of Bounded Sequences with Pointwise Addition and Pointwise Scalar Multiplication on Ring of Sequences forms Vector Space
- Space of Continuous on Closed Interval Real-Valued Functions with Pointwise Addition and Pointwise Scalar Multiplication forms Vector Space
- Space of Continuously Differentiable on Closed Interval Real-Valued Functions with Pointwise Addition and Pointwise Scalar Multiplication forms Vector Space
- Space of Integrable Functions is Vector Space
- Space of Square Summable Mappings is Vector Space

### T

### V

- Vector Space of All Mappings is Vector Space
- Vector Space of Sequences with Finite Support is Vector Space
- Vector Space on Cartesian Product is Vector Space
- Vector Space on Field Extension is Vector Space
- Vector Space over Division Subring is Vector Space
- Vector Space over Division Subring is Vector Space/Special Case
- Vector Space over Division Subring/Examples
- Vector Space over Division Subring/Examples/Real Numbers in Complex Numbers
- Vector Space/Examples
- Vector Space/Examples/Arrows through Point in 3D Space