Category:Definitions/Quaternions

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This category contains definitions related to Quaternions.
Related results can be found in Category: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:
\(\ds \mathbf i \mathbf j\) \(=\) \(\, \ds -\mathbf j \mathbf i \, \) \(\, \ds = \, \) \(\ds \mathbf k\)
\(\ds \mathbf j \mathbf k\) \(=\) \(\, \ds -\mathbf k \mathbf j \, \) \(\, \ds = \, \) \(\ds \mathbf i\)
\(\ds \mathbf k \mathbf i\) \(=\) \(\, \ds -\mathbf i \mathbf k \, \) \(\, \ds = \, \) \(\ds \mathbf j\)
\(\ds \mathbf i^2 = \mathbf j^2 = \mathbf k^2\) \(=\) \(\, \ds \mathbf i \mathbf j \mathbf k \, \) \(\, \ds = \, \) \(\ds -\mathbf 1\)

Subcategories

This category has only the following subcategory.

Q

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