Quaternion Arithmetic<br />Elmer Nocon<br />Angelo Bernabe<br />Mark Hitosis<br />
Quaternion Addition<br />Let<br />and<br />be two quaternions.<br />the sum of P and Q is <br />
Quaternion Addition<br />Let<br />and<br />be two quaternions.<br />the sum of P and Q is <br />
Quaternion Addition<br />Let<br />and<br />be two quaternions.<br />the sum of P and Q is <br />e5<br />
Quaternion Addition<br />Let<br />and<br />be two quaternions.<br />the sum of P and Q is <br />
Quaternion Addition<br />Let<br />and<br />be two quaternions.<br />the sum of P and Q is <br />e<br />
Quaternion Addition<br />Example:<br />Let<br />and<br />be two quaternions.<br />the sum of S and T is <br />
Quaternion Subtraction<br />Let<br />and<br />be two quaternions.<br />the difference of P and Q is <br />
Quaternion Subtraction<br />Let<br />and<br />be two quaternions.<br />the difference of P and Q is <br />
Quaternion Subtraction<br />Let<br />and<br />be two quaternions.<br />the difference of P and Q is <br />
Quaternion Subtraction<br />Let<br />and<br />be two quaternions.<br />the difference of P and Q is <br />
Quaternion Subtraction<br />Let<br />and<br />be two quaternions.<br />the difference of P and Q is <br />
Quaternion Subtraction<br />Example:<br />Let<br />and<br />be two quaternions.<br />the difference of S and T is <br />
Quaternion Multiplication<br />Let<br />and<br />be two quaternions.<br />the product of P and Q is <br />
Quaternion Multiplication<br />Let<br />and<br />be two quaternions.<br />the product of P and Q is <br />we distribute<br />
When we multiply the imaginary operators we use the following rules:<br />
When we multiply the imaginary operators we use the following rules:<br />
When we multiply the imaginary operators we use the following rules:<br />
then we simplify<br />our newly derived formula<br />
Quaternion Multiplication<br />Example:<br />Let<br />and<br />be two quaternions.<br />the product of S and T is <br />us...
Quaternion Division<br />Let<br />and<br />be two quaternions.<br />to find the quotient of P and Q <br />we need to multi...
Quaternion Conjugation<br />Let<br />be a quaternion.<br />the conjugate of P is <br />
Quaternion Conjugation<br />Example:<br />Let<br />be a quaternion.<br />the conjugate of P is <br />
Normal of a Quaternion<br />Let<br />be a quaternion.<br />the normal of P is <br />
Normal of a Quaternion<br />Example:<br />Let<br />be a quaternion.<br />the normal of P is <br />
Reciprocal of a Quaternion <br />Let<br />be a quaternion.<br />the reciprocal of P is <br />
Reciprocal of a Quaternion <br />Example:<br />Let<br />be a quaternion.<br />the reciprocal of P is <br />
Quaternion Division<br />Example:<br />Let<br />and<br />be two quaternions.<br />the quotient of P and Q is <br />
Quaternion Division<br />   we use our formula in quaternion multiplication<br />
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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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