1. Quaternion Arithmetic
Elmer Nocon
Angelo Bernabe
Mark Hitosis

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