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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:

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


$a, b, c, d$ are real numbers
$\mathbf 1, \mathbf i, \mathbf j, \mathbf k$ are entities related to each other in the following way:
\(\displaystyle \mathbf i \mathbf j = -\mathbf j \mathbf i\) \(=\) \(\displaystyle \mathbf k\)
\(\displaystyle \mathbf j \mathbf k = -\mathbf k \mathbf j\) \(=\) \(\displaystyle \mathbf i\)
\(\displaystyle \mathbf k \mathbf i = -\mathbf i \mathbf k\) \(=\) \(\displaystyle \mathbf j\)
\(\displaystyle \mathbf i^2 = \mathbf j^2 = \mathbf k^2 = \mathbf i \mathbf j \mathbf k\) \(=\) \(\displaystyle -\mathbf 1\)