# Category:Quaternions

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This category contains results about Quaternions.

Definitions specific to this category can be found in Definitions/Quaternions.

A **quaternion** is a number in the form:

- $a \mathbf 1 + b \mathbf i + c \mathbf j + d \mathbf k$

where:

- $a, b, c, d$ are real numbers

- $\mathbf 1, \mathbf i, \mathbf j, \mathbf k$ are entities related to each other in the following way:

\(\displaystyle \mathbf i \mathbf j = -\mathbf j \mathbf i\) | \(=\) | \(\displaystyle \mathbf k\) | |||||||||||

\(\displaystyle \mathbf j \mathbf k = -\mathbf k \mathbf j\) | \(=\) | \(\displaystyle \mathbf i\) | |||||||||||

\(\displaystyle \mathbf k \mathbf i = -\mathbf i \mathbf k\) | \(=\) | \(\displaystyle \mathbf j\) | |||||||||||

\(\displaystyle \mathbf i^2 = \mathbf j^2 = \mathbf k^2 = \mathbf i \mathbf j \mathbf k\) | \(=\) | \(\displaystyle -\mathbf 1\) |

## Subcategories

This category has the following 2 subcategories, out of 2 total.

### Q

## Pages in category "Quaternions"

The following 21 pages are in this category, out of 21 total.

### F

### M

### Q

- Quaternion Addition forms Abelian Group
- Quaternion Multiplication
- Quaternion Multplication is not Commutative
- Quaternions Defined by Ordered Pairs
- Quaternions form Algebra
- Quaternions form Skew Field
- Quaternions form Vector Space over Reals
- Quaternions form Vector Space over Themselves
- Quaternions Subring of Complex Matrix Space