Quaternion: Difference between revisions

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Here, <math>\mathbf{q}</math> represents the ''imaginary'' part: <math>q_1 \mathbf{i}+q_2 \mathbf{j}+q_3 \mathbf{k}</math>.
Here, <math>\mathbf{q}</math> represents the ''imaginary'' part: <math>q_1 \mathbf{i}+q_2 \mathbf{j}+q_3 \mathbf{k}</math>.


Conjugation is <math>\bar{q} = (q_0, -\mathbf{q})</math>.
The conjugate is <math>\bar{q} = (q_0, -\mathbf{q})</math>.


Multiplication is <math>q * p = (q_0 p_0 - \mathbf{q} \cdot \mathbf{p}, q_0 \mathbf{p} + p_0 \mathbf{q} + \mathbf{q} \times \mathbf{p})</math>.
Multiplication is <math>q * p = (q_0 p_0 - \mathbf{q} \cdot \mathbf{p}, q_0 \mathbf{p} + p_0 \mathbf{q} + \mathbf{q} \times \mathbf{p})</math>.