# 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 17 subcategories, out of 17 total.

### B

### D

### E

### G

### H

### I

- Inner Product Spaces (3 P)

### N

### Q

### S

- Scalar Addition (empty)
- Standard Ordered Bases (4 P)

### T

### V

## Pages in category "Vector Spaces"

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