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
- Definitions/Quaternion Group (3 P)
Pages in category "Definitions/Quaternions"
The following 22 pages are in this category, out of 22 total.
C
Q
- Definition:Quaternion
- Definition:Quaternion Addition
- Definition:Quaternion Conjugate/Quaternion Conjugation
- Definition:Quaternion Conjugation
- Definition:Quaternion Modulus
- Definition:Quaternion Modulus/Definition 1
- Definition:Quaternion Modulus/Definition 2
- Definition:Quaternion Multiplication
- Definition:Quaternion/Addition
- Definition:Quaternion/Algebra over Field
- Definition:Quaternion/Also denoted as
- Definition:Quaternion/Construction from Cayley-Dickson Construction
- Definition:Quaternion/Construction from Complex Pairs
- Definition:Quaternion/Multiplication