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# Quaternion arithmetic -

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### Quaternion arithmetic -

1. 1. Quaternion Arithmetic<br />Elmer Nocon<br />Angelo Bernabe<br />Mark Hitosis<br />
2. 2. Quaternion Addition<br />Let<br />and<br />be two quaternions.<br />the sum of P and Q is <br />
3. 3. Quaternion Addition<br />Let<br />and<br />be two quaternions.<br />the sum of P and Q is <br />
4. 4. Quaternion Addition<br />Let<br />and<br />be two quaternions.<br />the sum of P and Q is <br />e5<br />
5. 5. Quaternion Addition<br />Let<br />and<br />be two quaternions.<br />the sum of P and Q is <br />
6. 6. Quaternion Addition<br />Let<br />and<br />be two quaternions.<br />the sum of P and Q is <br />e<br />
7. 7. Quaternion Addition<br />Example:<br />Let<br />and<br />be two quaternions.<br />the sum of S and T is <br />
8. 8. Quaternion Subtraction<br />Let<br />and<br />be two quaternions.<br />the difference of P and Q is <br />
9. 9. Quaternion Subtraction<br />Let<br />and<br />be two quaternions.<br />the difference of P and Q is <br />
10. 10. Quaternion Subtraction<br />Let<br />and<br />be two quaternions.<br />the difference of P and Q is <br />
11. 11. Quaternion Subtraction<br />Let<br />and<br />be two quaternions.<br />the difference of P and Q is <br />
12. 12. Quaternion Subtraction<br />Let<br />and<br />be two quaternions.<br />the difference of P and Q is <br />
13. 13. Quaternion Subtraction<br />Example:<br />Let<br />and<br />be two quaternions.<br />the difference of S and T is <br />
14. 14. Quaternion Multiplication<br />Let<br />and<br />be two quaternions.<br />the product of P and Q is <br />
15. 15. Quaternion Multiplication<br />Let<br />and<br />be two quaternions.<br />the product of P and Q is <br />we distribute<br />
16. 16. When we multiply the imaginary operators we use the following rules:<br />
17. 17. When we multiply the imaginary operators we use the following rules:<br />
18. 18. When we multiply the imaginary operators we use the following rules:<br />
19. 19. then we simplify<br />our newly derived formula<br />
20. 20. Quaternion Multiplication<br />Example:<br />Let<br />and<br />be two quaternions.<br />the product of S and T is <br />using our formula<br />
21. 21. Quaternion Division<br />Let<br />and<br />be two quaternions.<br />to find the quotient of P and Q <br />we need to multiply P by the reciprocal of Q <br />and to find the Q-1, <br />we need to find the conjugate of q and divide it by the normal of q <br />
22. 22. Quaternion Conjugation<br />Let<br />be a quaternion.<br />the conjugate of P is <br />
23. 23. Quaternion Conjugation<br />Example:<br />Let<br />be a quaternion.<br />the conjugate of P is <br />
24. 24. Normal of a Quaternion<br />Let<br />be a quaternion.<br />the normal of P is <br />
25. 25. Normal of a Quaternion<br />Example:<br />Let<br />be a quaternion.<br />the normal of P is <br />
26. 26. Reciprocal of a Quaternion <br />Let<br />be a quaternion.<br />the reciprocal of P is <br />
27. 27. Reciprocal of a Quaternion <br />Example:<br />Let<br />be a quaternion.<br />the reciprocal of P is <br />
28. 28. Quaternion Division<br />Example:<br />Let<br />and<br />be two quaternions.<br />the quotient of P and Q is <br />
29. 29. Quaternion Division<br /> we use our formula in quaternion multiplication<br />
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