# 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.

## Pages in category "Quaternions"

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