Quaternion: Difference between revisions
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Quaternions are a number space that can be represented as a 4D point <math>q = (q_0, q_1, q_2, q_3) = (q_0, \mathbb{q})</math> with unit norm. Here, <math>\mathbf{q}</math> represented the ''imaginary'' part. | Quaternions are a number space that can be represented as a 4D point <math>q = (q_0, q_1, q_2, q_3) = (q_0, \mathbb{q})</math> with unit norm. Here, <math>\mathbf{q}</math> represented the ''imaginary'' part. | ||
Conjugation is <math>\bar{q} = (q_0, -\mathbf{q}</math>. | Conjugation 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>. | ||