Category:Quaternions
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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:
- $a \mathbf 1 + b \mathbf i + c \mathbf j + d \mathbf k$
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 the following 2 subcategories, out of 2 total.
Q
- Quaternion Modulus (4 P)
Pages in category "Quaternions"
The following 21 pages are in this category, out of 21 total.
F
M
Q
- Quaternion Addition forms Abelian Group
- Quaternion Multiplication
- Quaternion Multplication is not Commutative
- Quaternions Defined by Ordered Pairs
- Quaternions form Algebra
- Quaternions form Skew Field
- Quaternions form Vector Space over Reals
- Quaternions form Vector Space over Themselves
- Quaternions Subring of Complex Matrix Space