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Quaternion: Difference between revisions
→Multiplication
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Similar to imaginary numbers, <math>\mathbf{i}^2=\mathbf{j}^2=\mathbf{k}^2=\mathbf{i}\mathbf{j}\mathbf{k}=-1</math>. | Similar to imaginary numbers, <math>\mathbf{i}^2=\mathbf{j}^2=\mathbf{k}^2=\mathbf{i}\mathbf{j}\mathbf{k}=-1</math>. | ||
Multiplication between bases follow cross product rules: <math>\mathbf{i} * \mathbf{j} = \mathbf{k}</math> and <math>\mathbf{j} * \mathbf{i} = -\mathbf{k}</math>. | Multiplication between bases follow cross product rules: <math>\mathbf{i} * \mathbf{j} = \mathbf{k}</math> and <math>\mathbf{j} * \mathbf{i} = -\mathbf{k}</math>. | ||
In general, quaternion multiplication does not commute: <math>q_1 * q_2 \neq q_2 * q_1</math> | |||
Intuition: Left multiplication by a quaternion is a 4D rotation plus a scaling operation. | Intuition: Left multiplication by a quaternion is a 4D rotation plus a scaling operation. | ||