# Category:Quaternions

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 19 pages are in this category, out of 19 total.