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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:
|\(\displaystyle \mathbf i \mathbf j = -\mathbf j \mathbf i\)||\(=\)||\(\displaystyle \mathbf k\)|
|\(\displaystyle \mathbf j \mathbf k = -\mathbf k \mathbf j\)||\(=\)||\(\displaystyle \mathbf i\)|
|\(\displaystyle \mathbf k \mathbf i = -\mathbf i \mathbf k\)||\(=\)||\(\displaystyle \mathbf j\)|
|\(\displaystyle \mathbf i^2 = \mathbf j^2 = \mathbf k^2 = \mathbf i \mathbf j \mathbf k\)||\(=\)||\(\displaystyle -\mathbf 1\)|
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.
- 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