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Quaternion arithmetic -
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
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