Reciprocal
If
then its reciprocal is defined as
The expression:
Reciprocals have many important applications, for example rotations, particularly when q is a versor. A versor has an easy formula for its reciprocal.
In words the reciprocal of a versor is equal to its conjugate. The dots between operators show the order to of the operations, and also help to indicate that S and U for example, are two different operations rather than a single operation named SU.
Read more about this topic: Classical Hamiltonian Quaternions, Other Operators in Detail
Famous quotes containing the word reciprocal:
“I had no place in any coterie, or in any reciprocal self-advertising. I stood alone. I stood outside. I wanted only to learn. I wanted only to write better.”
—Ellen Glasgow (1873–1945)
“Parenting is a profoundly reciprocal process: we, the shapers of our children’s lives, are also being shaped. As we struggle to be parents, we are forced to encounter ourselves; and if we are willing to look at what is happening between us and our children, we may learn how we came to be who we are.”
—Augustus Y. Napier (20th century)
“Of course we will continue to work for cheaper electricity in the homes and on the farms of America; for better and cheaper transportation; for low interest rates; for sounder home financing; for better banking; for the regulation of security issues; for reciprocal trade among nations and for the wiping out of slums. And my friends, for all of these we have only begun to fight.”
—Franklin D. Roosevelt (1882–1945)