Proposition: If and , then is a pure quaternion.

Proof: Let , with and ( is a pure quaternion).

Then . The key observation is that if , then .

Since , this means that , i.e. , so is a pure quaternion.

Advertisements

Advertisements

Proposition: If and , then is a pure quaternion.

Proof: Let , with and ( is a pure quaternion).

Then . The key observation is that if , then .

Since , this means that , i.e. , so is a pure quaternion.

Advertisements

%d bloggers like this: