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Quaternion: Difference between revisions
→Double Quaternions
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Any 4D rotation matrix can be decomposed into a right and a left isoclinic rotation matrix: | Any 4D rotation matrix can be decomposed into a right and a left isoclinic rotation matrix: | ||
<math>R = R^L R^R = R^R R^L</math> | <math>R = R^L R^R = R^R R^L</math> | ||
<math>R^R</math> and <math>R^L</math> can be | <math>R^R</math> and <math>R^L</math> can be viewed as a matrix representation of single double quaternion <math>(q_1, q_2)</math>. | ||
For a double quaternion, the 4D rotation written is <math>x' = q_1 x q_2</math>. | |||
The product of left and right isoclinic rotation matrices commute. | The product of left and right isoclinic rotation matrices commute. | ||